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- R. Adami - U. Boscain - V. Franceschi - D. Prandi (Submitted Paper)

Point interactions for 3D sub-Laplacians (2019) - D. Addona - G. Menegatti - M. Miranda Jr (Submitted Paper)

Characterization of BV functions on open domains: the Gaussian case and the general case (2019) - C. Afeltra (preprint)

Singular periodic solutions to a critical equation in the Heisenberg group (2019) - V. Agostiniani - M. Fogagnolo - L. Mazzieri (preprint)

Minkowski Inequalities via Nonlinear Potential Theory (2019) - A. Agrachev - D. Barilari - U. Boscain (Lecture Notes:
*Cambridge Studies in Advanced Mathematics*)

A Comprehensive Introduction to Sub-Riemannian Geometry (2019) - G. Alberti - G. Buttazzo - S. Guarino Lo Bianco - E. Oudet (Accepted Paper:
*Networks and Heterogeneous Media*)

Optimal reinforcing networks for elastic membranes (2019) - G. Alberti - A. Massaccesi - E. Stepanov (Submitted Paper)

On the geometric structure of currents tangent to smooth distributions (2019) - G. Albi - M. Bongini - F. Rossi - F. Solombrino (
*Mathematical Models and Methods in Applied Sciences*)

Leader formation with mean-field birth and death models (2019) - F. Alessio - P. Montecchiari - A. Zuniga (Submitted Paper)

Prescribed-energy connecting orbits for gradient systems (2019) - S. Almi - G. Lazzaroni - I. Lucardesi (Preprint)

Crack growth by vanishing viscosity in planar elasticity (2019) - L. Ambrosio - F. Glaudo - D. Trevisan (Preprint)

On the optimal map in the 2-dimensional random matching problem (2019) - D. Pallara - L. Angiuli - S. Ferrari (Accepted Paper:
*J. Evol. Equ.*)

Gradient estimates for perturbed Ornstein-Uhlenbeck semigroups on infinite dimensional convex domains (2019) - N. Ansini - A. Braides - J. Zimmer (
*Proc. Roy. Soc. Edinburgh A*)

Minimising movements for oscillating energies: the critical regime (2019) - N. Ansini - S. Fagioli (Submitted Paper)

Nonlinear diffusion equations with degenerate fast-decay mobility by coordinate transformation (2019) - G. Antonelli - E. Bruè - D. Semola (Submitted Paper)

Volume bounds for the quantitative singular strata of non collapsed RCD metric measure spaces (2019) - A. H. Ardila - L. Cely - M. Squassina (Accepted Paper:
*Asymptotic Anal.*)

Logarithmic Bose-Einstein condensates with harmonic potential (2019) - A. Arroyo-Rabasa (preprint)

Characterization of generalized Young measures generated by $\mathcal A$-free measures (2019) - A. Arroyo-Rabasa - J. Diermeier (preprint)

Generalized multi-scale Young measures (2019) - J. F. Babadjian - F. Iurlano - A. Lemenant (Preprint)

Partial regularity for the crack set minimizing the two-dimensional Griffith energy (2019) - J. F. Babadjian - F. Iurlano - F. Rindler (Preprint)

Concentration versus oscillation effects in brittle damage (2019) - A. Bach - A. Braides - M. Cicalese (Preprint)

Discrete-to-continuum limits of multi-body systems with bulk and surface long-range interactions (2019) - A. Bach - M. Cicalese - M. Ruf (preprint)

Random finite-difference discretizations of the Ambrosio-Tortorelli functional with optimal mesh size (2019) - A. Bach - L. Sommer (Preprint)

A $\Gamma$-convergence result for fluid-filled fracture propagation (2019) - A. Baldi - B. Franchi - P. Pansu (Submitted Paper)

{$L^1$-{P}oincar\'e inequalities for differential forms on {E}uclidean spaces and {H}eisenberg groups} (2019) - M. Bardi - A. Cesaroni - E. Topp (Accepted Paper:
*Proc. Roy. Soc. Edinburgh Sect. A*)

Cauchy problem and periodic homogenization for nonlocal Hamilton-Jacobi equations with coercive gradient terms (2019) - M. Bardi - A. Goffi (Submitted Paper)

New strong maximum and comparison principles for fully nonlinear degenerate elliptic PDEs (2019) - D. Barilari - S. Ivanov (
*Calc. Var. PDE*)

A Bonnet-Myers type theorem for quaternionic contact structures (2019) - D. Barilari - L. Rizzi (Preprint)

Bakry-Émery curvature and model spaces in sub-Riemannian geometry (2019) - D. Bartolucci - C. Gui - Y. Hu - A. Jevnikar - W. Yang (Accepted Paper:
*Discrete Contin. Dyn. Syst.*)

Mean field equations on tori: existence and uniqueness of evenly symmetric blow-up solutions (2019) - D. Bartolucci - A. Jevnikar (Preprint)

On the global bifurcation diagram of the Gel'fand problem (2019) - D. Bartolucci - A. Jevnikar - Y. Lee - W. Yang (Preprint)

Local uniqueness and non-degeneracy of blow up solutions of mean field equations with singular data (2019) - G. Bellettini - A. Elshorbagy (Submitted Paper)

On the square distance function from a manifold with boundary (2019) - G. Bellettini - A. Elshorbagy - M. Paolini - R. Scala (Preprint)

On the relaxed area of the graph of discontinuous maps from the plane to the plane taking three values with no symmetry assumptions (2019) - V. Benci - S. Nardulli - P. Piccione (Submitted Paper)

Multiple solutions for the Van der Waals--Allen--Cahn--Hilliard equation with a volume constraint (2019) - G. Bevilacqua - L. Lussardi - A. Marzocchi (Submitted Paper)

Dimensional reduction of the Kirchhoff-Plateau problem (2019) - G. Bevilacqua - L. Lussardi - A. Marzocchi (
*Quart. Appl. Math.*)

Soap film spanning an elastic link (2019) - S. Biagi - G. Cupini - E. Mascolo (Submitted Paper)

Regularity of quasi-minimizers for non-uniformly elliptic integrals (2019) - S. Bianchini - P. Bonicatto (Proceedings)

Untangling of trajectories for non-smooth vector fields and Bressan's Compactness Conjecture (2019) - U. Bindini (preprint)

Smoothing operators in multi-marginal Optimal Transport (2019) - U. Bindini - L. De Pascale (preprint)

From wave-functions to single electron densities (2019) - M. Bonafini - M. Novaga - G. Orlandi (
*Nonlinear Analysis*)

A variational scheme for hyperbolic obstacle problems (2019) - M. Bonafini - G. Orlandi - E. Oudet (Submitted Paper)

Variational approximation of functionals defined on 1-dimensional connected sets in $\mathbb{R}^n$ (2019) - G. A. Bonaschi - R. Rossi (Accepted Paper:
*Annali di Matematica Pura ed Applicata*)

Generation of Balanced Viscosity solutions to rate-independent systems via variational convergence (2019) - M. Bonforte - A. Figalli (Accepted Paper:
*Comm. Pure Appl. Math.*)

Sharp Extinction Rates for Fast Diffusion Equations on Generic Bounded Domains (2019) - P. Bonicatto - E. Pasqualetto - T. Rajala (Preprint)

Indecomposable sets of finite perimeter in doubling metric measure spaces (2019) - G. Bouchitté - G. Buttazzo - T. Champion - L. De Pascale (Preprint)

Relaxed multi-marginal costs and quantization effects (2019) - P. Bousquet - L. Brasco (Accepted Paper:
*Rev. Mat. Iberoam.*)

Lipschitz regularity for orthotropic functionals with nonstandard growth conditions (2019) - J. E. M. Braga - A. Figalli - D. Moreira (Accepted Paper:
*Comm. Math. Phys.*)

Optimal regularity for the convex envelope and semiconvex functions related to supersolutions of fully nonlinear elliptic equations (2019) - A. Braides - P. Cermelli - S. Dovetta (Accepted Paper:
*ESAIM: Control, Optimization and Calculus of Variations*)

$\Gamma$-limit of the cut functional on dense graph sequences (2019) - A. Braides - V. Chiadò Piat (
*Applicable Analysis*)

Homogenization of networks in domains with oscillating boundaries (2019) - A. Braides - N. A. Nodargi (Accepted Paper:
*Math. Mech. Solids*)

Homogenization of cohesive fracture in masonry structures (2019) - A. Braides - A. Tribuzio (Submitted Paper)

Perturbed minimizing movements of families of functionals (2019) - L. Brasco (Accepted Paper:
*Ann. Fac. Sci. Toulouse Math.*)

On principal frequencies and isoperimetric ratios in convex sets (2019) - L. Brasco - E. Cinti - S. Vita (Preprint)

A quantitative stability estimate for the fractional Faber-Krahn inequality (2019) - L. Brasco - G. Franzina (Preprint)

An overview on constrained critical points of Dirichlet integrals (2019) - L. Brasco - E. Lindgren - M. Stromqvist (Preprint)

Continuity of solutions to a nonlinear fractional diffusion equation (2019) - K. Bredies - M. Carioni - S. Fanzon - F. Romero (Submitted Paper)

On the extremal points of the ball of the Benamou-Brenier energy (2019) - K. Bredies - S. Fanzon (Submitted Paper)

An optimal transport approach for solving dynamic inverse problems in spaces of measures (2019) - E. Bruè - Q. H. Nguyen (Preprint)

Sobolev estimates for solutions of the transport equation and ODE flows associated to non-Lipschitz drifts (2019) - C. Bucur - M. Squassina (Preprint)

Approximate convexity principles and applications to PDEs in convex domains (2019) - D. Bucur - I. Fragalà - A. Giacomini (Submitted Paper)

The Multiphase Mumford-Shah Problem (2019) - D. Bucur - A. Giacomini - P. Trebeschi (Submitted Paper)

$L^\infty$ bounds of Steklov eigenfunctions and spectrum stability under domain variation (2019) - V. Buffa - G. E. Comi - M. Miranda Jr (Submitted Paper)

On $BV$ functions and essentially bounded divergence-measure fields in metric spaces (2019) - V. Buffa - M. Miranda Jr (Submitted Paper)

Rough traces of $BV$ functions in metric measure spaces (2019) - L. Bungert - M. Burger - A. Chambolle - M. Novaga (Submitted Paper)

Nonlinear Spectral Decompositions by Gradient Flows of One-Homogeneous Functionals (2019) - F. Cagnetti (Accepted Paper:
*Portugaliae Mathematica*)

Rigidity for Perimeter Inequalities under symmetrization: state of the art and open problems (2019) - F. Cagnetti - G. Dal Maso - L. Scardia - C. I. Zeppieri (Accepted Paper:
*Arch. Ration. Mech. Anal.*)

Stochastic Homogenisation of Free-Discontinuity Problems (2019) - F. Cagnetti - M. Perugini - D. Stöger (Submitted Paper)

Rigidity for perimeter inequality under spherical symmetrisation (2019) - F. Camilli - A. Goffi (Submitted Paper)

Existence and regularity results for viscous Hamilton-Jacobi equations with Caputo time-fractional derivative (2019) - G. Canevari - G. Orlandi (Submitted Paper)

Lifting for manifold-valued maps of bounded variation (2019) - G. Canevari - G. Orlandi (Accepted Paper:
*Calc. Var. PDE*)

Topological singular set of vector-valued maps, I: Applications to manifold-constrained Sobolev and BV spaces (2019) - P. Cannarsa - G. Floridia - F. F. G\"olgeleyen - M. Yamamoto (Preprint)

Inverse coefficient problems for a transport equation by local Carleman estimate (2019) - P. Cannarsa - G. Floridia - F. G\"olgeleyen - M. Yamamoto (Preprint)

Inverse coefficient problems for a transport equation by local Carleman estimate (2019) - P. Cannarsa - G. Floridia - F. G\"olgeleyen - M. Yamamoto (Preprint)

Inverse coefficient problems for a transport equation by local Carleman estimate (2019) - A. Pinamonti - G. Speight - M. Capolli (Submitted Paper)

A $C^m$ Lusin Approximation Theorem for Horizontal Curves in the Heisenberg Group (2019) - M. Caponi - F. Sapio (Submitted Paper)

A dynamic model for viscoelastic materials with prescribed growing cracks (2019) - M. Carioni - A. Marchese - A. Massaccesi - A. Pluda - R. Tione (Submitted Paper)

The oriented mailing problem and its convex relaxation (2019) - M. Carioni - A. Pluda (Accepted Paper:
*ESAIM Control Optim. Calc. Var.*)

Calibrations for minimal networks in a covering space setting (2019) - M. Carioni - A. Pluda (Accepted Paper:
*Adv. Calc. Var.*)

On different notions of calibrations for minimal partitions and minimal networks in $\mathbb{R}^2$ (2019) - M. Caroccia - A. Chambolle - D. Slepčev (Submitted Paper)

Mumford - Shah on graphs and their asymptotics (2019) - M. Caroccia - M. Focardi - N. Van Goethem (Submitted Paper)

On the integral representation of variational functionals on $BD$ (2019) - M. Caroccia - N. Van Goethem (Accepted Paper:
*ESAIM: M2AN*)

Damage-driven fracture with low-order potentials: asymptotic behavior, existence and applications (2019) - J. A. Carrillo - J. Mateu - M. G. Mora - L. Rondi - L. Scardia - J. Verdera (Accepted Paper:
*Commun. Math. Phys.*)

The ellipse law: Kirchhoff meets dislocations (2019) - J. A. Carrillo - J. Mateu - M. G. Mora - L. Rondi - L. Scardia - J. Verdera (Preprint)

The equilibrium measure for an anisotropic nonlocal energy (2019) - G. Catino - F. Gazzola - P. Mastrolia (Submitted Paper)

A conformal Yamabe problem with potential on the Euclidean space (2019) - G. Catino - P. Mastrolia (
*Ann. Glob. Anal. Geom.*)

A potential generalization of some canonical Riemannian metrics (2019) - G. Catino - D. D. Monticelli - F. Punzo (Submitted Paper)

The Poisson equation on Riemannian manifolds with weighted Poincaré inequality at infinity (2019) - G. Catino - D. D. Monticelli - F. Punzo (Accepted Paper:
*Calc. Var. Partial Differential Equations*)

The Poisson equation on manifolds with positive essential spectrum (2019) - G. Catino - A. Roncoroni - L. Vezzoni (Submitted Paper)

On the umbilic set of immersed surfaces in three-dimensional space forms (2019) - A. Cesaroni - M. Cirant - S. Dipierro - M. Novaga - E. Valdinoci (
*J. Math. Pures Appl.*)

On stationary fractional Mean Field Games (2019) - A. Cesaroni - S. Dipierro - M. Novaga - E. Valdinoci (Accepted Paper:
*Math. Ann.*)

Fattening and nonfattening phenomena for planar nonlocal curvature flows (2019) - A. Chambolle - L. Lussardi - E. Villa (Submitted Paper)

Anisotropic tubular neighborhoods of sets (2019) - A. Chambolle - M. Morini - M. Novaga - M. Ponsiglione (
*J. Amer. Math. Soc.*)

Existence and uniqueness for anisotropic and crystalline mean curvature flows (2019) - A. Chambolle - M. Morini - M. Novaga - M. Ponsiglione (
*Anal. PDE*)

Generalized crystalline evolutions as limits of flows with smooth anisotropies (2019) - A. Chambolle - M. Novaga - V. Pagliari (Preprint)

On the convergence rate of some nonlocal energies (2019) - G. Q. Chen - G. E. Comi - M. Torres (
*Arch. Ration. Mech. Anal.*)

Cauchy Fluxes and Gauss-Green Formulas for Divergence-Measure Fields over General Open Sets (2019) - J. H. Cheng - A. Malchiodi - P. Yang (Submitted Paper)

On the Sobolev quotient of three-dimensional CR manifolds (2019) - Y. Chitour - D. Prandi - L. Rizzi (Preprint)

Weyl's law for singular Riemannian manifolds (2019) - M. Cicalese - M. Forster - G. Orlando (preprint)

Variational analysis of a two-dimensional frustrated spin system: emergence and rigidity of chirality transitions (2019) - M. Cicalese - G. P. Leonardi (Submitted Paper)

Maximal fluctuations on periodic lattices: an approach via quantitative Wulff inequalities (2019) - M. Cicalese - G. Orlando - M. Ruf (Preprint)

From the $N$-clock model to the $XY$ model: emergence of concentration effects in the variational analysis (2019) - E. Cinti - F. Colasuonno (preprint)

A nonlocal supercritical Neumann problem (2019) - G. Ciraolo - A. Figalli - A. Roncoroni (Submitted Paper)

Symmetry results for critical anisotropic $p$-Laplacian equations in convex cones (2019) - S. Cito (
*Journal of Convex Analysis*)

Existence and Regularity of Optimal Convex Shapes for Functionals Involving the Robin Eigenvalues (2019) - M. Colombo - A. De Rosa - A. Marchese (Submitted Paper)

On the well-posedness of branched transportation (2019) - S. Di Marino - F. Stra - M. Colombo (Submitted Paper)

Continuity of multi-marginal optimal transport with repulsive cost (2019) - M. Colombo - L. Spolaor - B. Velichkov (Preprint)

Almost everywhere uniqueness of blow-up limits for the lower dimensional obstacle problem (2019) - G. E. Comi - G. Stefani (Accepted Paper:
*Journal of Functional Analysis*)

A distributional approach to fractional Sobolev spaces and fractional variation: existence of blow-up (2019) - D. Cordero-Erausquin - A. Figalli (Accepted Paper:
*Discrete Contin. Dyn. Syst.*)

Regularity of monotone transport maps between unbounded domains (2019) - G. Crasta - V. De Cicco - A. Malusa (Preprint)

Pairings between bounded divergence-measure vector fields and BV functions (2019) - A. Malusa - G. Crasta (Accepted Paper:
*Symmetry*)

Non-coercive radially symmetric variational problems: existence, symmetry and convexity of minimizers (2019) - V. Crismale (Accepted Paper:
*Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl.*)

Density in $SBD$ and approximation of fracture energies (2019) - G. Cupini - M. Focardi - F. Leonetti - E. Mascolo (Accepted Paper:
*Adv. Nonlinear Anal.*)

On the H\"older continuity for a class of vectorial problems (2019) - G. Cupini - N. Fusco - E. Lanconelli - X. Zhong (Accepted Paper:
*J. Anal. Math.*)

A sharp stability result for the Gauss mean value formula (2019) - G. Cupini - E. Lanconelli (Submitted Paper)

On Mean Value formulas for solutions to linear second order PDEs (2019) - E. Davoli - G. Di Fratta (Submitted Paper)

Homogenization of chiral magnetic materials - A mathematical evidence of Dzyaloshinskii's predictions on helical structures (2019) - E. Davoli - R. Ferreira - C. Kreisbeck (Submitted Paper)

Homogenization in $BV$ of a model for layered composites in finite crystal plasticity (2019) - E. Davoli - I. Fonseca - P. Liu (Submitted Paper)

Adaptive image processing: first order PDE constraint regularizers and a bilevel training scheme (2019) - E. Davoli - H. Ranetbauer - L. Scarpa - L. Trussardi (Submitted Paper)

Degenerate nonlocal Cahn-Hilliard equations: well-posedness, regularity and local asymptotics (2019) - E. Davoli - T. Roubicek - U. Stefanelli (Accepted Paper:
*ZAMM - Zeitschrift für Angewandte Mathematik und Mechanik*)

Dynamic perfect plasticity and damage in viscoelastic solids (2019) - E. Davoli - L. Scarpa - L. Trussardi (Submitted Paper)

Nonlocal-to-local convergence of Cahn-Hilliard equations: Neumann boundary conditions and viscosity terms (2019) - E. Davoli - U. Stefanelli (Accepted Paper:
*SIAM Journal on Mathematical Analysis*)

Dynamic perfect plasticity as convex minimization (2019) - F. Dayrens - S. Masnou - M. Novaga - M. Pozzetta (Submitted Paper)

Connected perimeter of planar sets (2019) - V. De Cicco - D. Giachetti - F. Oliva - F. Petitta (Accepted Paper:
*Calc. Var. Partial Differential Equations*)

Dirichlet problems for singular elliptic equations with general nonlinearities (2019) - C. De Filippis - G. Palatucci (
*J. Differential Equations*)

Hölder regularity for nonlocal double phase equations (2019) - C. De Lellis - G. De Philippis - J. Hirsch (Submitted Paper)

Nonclassical minimizing surfaces with smooth boundary (2019) - C. De Lellis - L. J. Székelyhidi (Accepted Paper:
*To appear in the Notices of the AMS*)

On turbulence and geometry: from Nash to Onsager (2019) - C. De Lellis - Z. Zhao (Preprint)

Dirichlet energy-minimizers with analytic boundary (2019) - L. De Luca - M. Novaga - M. Ponsiglione (
*J. Nonlinear Sci.*)

$\Gamma$-convergence of the Heitmann-Radin sticky disc energy to the crystalline perimeter (2019) - L. De Luca - M. Novaga - M. Ponsiglione (Preprint)

The $0$-fractional perimeter between fractional perimeters and Riesz potentials (2019) - N. De Nitti - J. Fischer (preprint)

Sharp criteria for the waiting time phenomenon in solutions to the thin-film equation (2019) - G. De Philippis - A. De Rosa - J. Hirsch (
*Discrete Contin. Dyn. Syst.*)

The area blow up set for bounded mean curvature submanifolds with respect to elliptic surface energy functionals (2019) - G. De Philippis - J. Hirsch - G. Vescovo (Submitted Paper)

Regularity of minimizers for a model of charged droplets (2019) - G. De Philippis - M. Marini - E. Mukoseeva (Submitted Paper)

The sharp quantitative isocapacitary inequality (2019) - N. De Ponti (preprint)

Metric properties of homogeneous and spatially inhomogeneous F-divergences (2019) - N. De Ponti - A. Mondino (Preprint)

Sharp Cheeger-Buser type inequalities in $RCD(K,\infty)$ spaces (2019) - N. De Ponti - M. Muratori - C. Orrieri (preprint)

Wasserstein stability of porous medium-type equations on manifolds with Ricci curvature bounded below (2019) - A. De Rosa - L. Lussardi (Submitted Paper)

On the anisotropic Kirchhoff-Plateau problem (2019) - C. Debin - N. Gigli - E. Pasqualetto (Submitted Paper)

Quasi-continuous vector fields on $\sf RCD$ spaces (2019) - M. Degiovanni - D. Mazzoleni (Preprint)

Optimization results for the higher eigenvalues of the $p$-Laplacian associated with sign-changing capacitary measures (2019) - G. Del Nin (Preprint)

Some asymptotic results on the global shape of planar clusters (2019) - G. Del Nin - A. Pluda - M. Pozzetta (Preprint)

Degenerate elastic networks (2019) - D. Di Donato (preprint)

Intrinsic Lipschitz graphs in Carnot groups of step 2 (2019) - G. Di Fratta - A. Fiorenza (Preprint)

BMO-type seminorms from Escher-type tessellations (2019) - G. Di Fratta - C. Muratov - F. Rybakov - V. Slastikov (Preprint)

Variational principles of micromagnetics revisited (2019) - S. Dipierro - M. Novaga - E. Valdinoci (
*J. London Math. Soc.*)

On a Minkowski geometric flow in the plane: Evolution of curves with lack of scale invariance (2019) - N. Dirr - F. Dragoni - P. Mannucci - C. Marchi (Preprint:
*Submitted paper*)

$\Gamma$- convergence and homogenisation for a class of degenerate functionals. (2019) - F. Dragoni - D. Filali (
*Journal of Convex Analysis*)

Starshaped and convex sets in Carnot groups and in the geometries of vector fields. (2019) - S. Dweik (Accepted Paper:
*Communications on Pure and Applied Analysis*)

$L^{p,q}$ estimates on the transport density (2019) - S. Dweik - N. Ghoussoub - A. Z. Palmer (Accepted Paper:
*Journal of Dynamical and Control Systems*)

Optimal controlled transports with free end times subject to import/export tariffs (2019) - S. Dweik - W. Górny (Submitted Paper)

Least gradient problem on annuli (2019) - S. Dweik - G. Mazanti (Submitted Paper)

Sharp semi-concavity in a non-autonomous control problem and $L^p$ estimates in an optimal-exit MFG (2019) - P. Esposito - A. Malchiodi (Preprint)

CRITICAL METRICS FOR LOG-DETERMINANT FUNCTIONALS IN CONFORMAL GEOMETRY (2019) - S. Fanzon - M. Ponsiglione - R. Scala (Submitted Paper)

Uniform distribution of dislocations in Peierls-Nabarro models for semi-coherent interfaces (2019) - F. Farroni - N. Fusco - S. Guarino Lo Bianco - R. Schiattarella (Submitted Paper)

A formula for the anisotropic total variation of SBV functions (2019) - R. Ferreira - D. Gomes - X. Yang (Preprint)

Two-scale homogenization of a stationary mean-field game (2019) - R. Ferreira - E. Zappale (preprint:
*Comm. Pure Appl. Anal.*)

Bending-torsion moments in thin multi-structures in the context of nonlinear elasticity (2019) - A. Figalli - D. Jerison (Accepted Paper:
*Ann. Sci. Éc. Norm. Supér.*)

A sharp Freiman type estimate for semisums in two and three dimensional Euclidean spaces (2019) - A. Figalli - M. J. Kang (Accepted Paper:
*Anal. PDE*)

A rigorous derivation from the kinetic cucker-smale model to the pressureless euler system with nonlocal alignment (2019) - A. Figalli - J. Serra (Accepted Paper:
*Invent. Math.*)

On stable solutions for boundary reactions: a De Giorgi-type result in dimension 4+1 (2019) - A. Figalli - J. Serra (Accepted Paper:
*Invent. Math.*)

On the fine structure of the free boundary for the classical obstacle problem (2019) - M. Focardi - E. Spadaro (Submitted Paper)

The local structure of the free boundary in the fractional obstacle problem (2019) - V. Franceschi - D. Prandi (Submitted Paper)

Hardy-type inequalities for the Carnot-Carathéodory distance in the Heisenberg group (2019) - V. Franceschi - D. Prandi - L. Rizzi (
*Potential Anal.*)

On the essential self-adjointness of singular sub-Laplacians (2019) - E. Fried - L. Lussardi (
*Rend. Lincei Mat. Appl.*)

Monotonicity formulae for smooth extremizers of integral functionals (2019) - L. Kreutz - M. Friedrich (Submitted Paper)

Finite crystallization and wulff shape emergence for ionic compounds in the square lattice (2019) - M. Friedrich - F. Solombrino (Preprint)

Functionals defined on piecewise rigid functions: Integral representation and $\Gamma$-convergence (2019) - G. Fusco - G. F. Gronchi - M. Novaga (
*Minimax Theory Appl.*)

Existence of periodic orbits near heteroclinic connections (2019) - N. Fusco - S. Mukherjee - Y. R. Y. Zhang (
*Proc. London Math. Soc.*)

A variational characterisation of the second eigenvalue of the p-Laplacian on quasi open sets (2019) - H. Garcke - J. Menzel - A. Pluda (Preprint)

Long Time Existence of Solutions to an Elastic Flow of Networks (2019) - H. Garcke - J. Menzel - A. Pluda (
*J. Differential Equations*)

Willmore flow of planar networks (2019) - A. Gerolin - A. Kausamo - T. Rajala (Preprint)

Multi-marginal Entropy-Transport with repulsive cost (2019) - A. Gerolin - A. Kausamo - T. Rajala (
*SIAM Journal on Mathematical Analysis*)

Non-existence of optimal transport maps for the multi-marginal repulsive harmonic cost (2019) - N. Gigli (Preprint)

Riemann curvature tensor on RCD spaces and possible applications (2019) - N. Gigli - A. Tyulenev (Preprint)

Korevaar-Schoen's directional energy and Ambrosio's regular Lagrangian flows (2019) - P. Gladbach - H. Olbermann (preprint)

Coarea formulae and chain rules for the Jacobian determinant in fractional Sobolev spaces (2019) - P. Gladbach - H. Olbermann (preprint)

Energy scaling for a conically constrained sector (2019) - M. Goldman (Proceedings:
*Actes du Séminaire Laurent Schwartz*)

A variational approach to regularity theory in optimal transportation (2019) - M. Goldman - M. Huesmann - F. Otto (Preprint)

Quantitative linearization results for the Monge-Ampère equation (2019) - M. Goldman - B. Merlet (Preprint)

Non-convex functionals penalizing simultaneous oscillations along independent directions: rigidity estimates (2019) - P. J. Graber - A. R. Mészáros - F. Silva - D. Tonon (Accepted Paper:
*Calc. Var. Partial Differential Equations*)

The planning problem in Mean Field Games as regularized mass transport (2019) - D. Grandi - M. Kruzik - E. Mainini - U. Stefanelli (
*Arch. Ration. Mech. Anal.*)

A phase-field approach to Eulerian interfacial energies (2019) - B. Han (Preprint)

Measure rigidity of synthetic lower Ricci curvature bound on Riemannian manifolds (2019) - B. Han (Accepted Paper:
*Manuscripta Mathematica*)

The sharp $p$-Poincaré inequality under the measure contraction property (2019) - B. Han - E. Milman (Preprint)

Sharp Poincare inequality under Measure Contraction Property (2019) - B. Han - K. T. Sturm (preprint)

Curvature-dimension conditions for diffusions under time change (2019) - J. Hirsch - S. Stuvard - D. Valtorta (
*Trans. Amer. Math. Soc.*)

Rectifiability of the singular set of multiple valued energy minimizing harmonic maps (2019) - A. Iannizzotto - S. J. N. Mosconi - M. Squassina (Preprint)

Sobolev versus Holder minimizers for the degenerate fractional $p$-Laplacian (2019) - M. Jacobs - I. Kim - A. R. Mészáros (Submitted Paper)

Weak solutions to the Muskat problem with surface tension via optimal transport (2019) - P. Lahti - R. Jones - N. Shanmugalingam (Accepted Paper:
*Indiana University Math. J.*)

Modulus of families of sets of finite perimeter and quasiconformal maps between metric spaces of globally $Q$-bounded geometry (2019) - V. Julin - D. A. La Manna (Preprint)

Short time existence of the classical solution to the fractional mean curvature flow (2019) - V. Kapovitch - A. Mondino (Preprint)

On the topology and the boundary of $N$-dimensional $RCD(K,N)$ spaces (2019) - S. Kholmatov - P. Piovano (Submitted Paper)

A unified model for stress-driven rearrangement instabilities (2019) - D. King - F. Maggi - S. Stuvard (Preprint)

Plateau's problem as a singular limit of capillarity problems (2019) - S. Krantz - M. Peloso - D. Spector (Preprint)

Some remarks on $L^1$ embeddings in the subelliptic setting (2019) - C. Kreisbeck - E. Zappale (Preprint)

Loss of double-integral character during relaxation (2019) - C. Kreisbeck - E. Zappale (Preprint)

Lower semicontinuity and relaxation of nonlocal $L^\infty$-functionals (2019) - L. Kreutz - P. Piovano (Submitted Paper)

Microscopic validation of a variational model of epitaxially strained crystalline films (2019) - D. Kwon - A. R. Mészáros (Submitted Paper)

Degenerate nonlinear parabolic equations with discontinuous diffusion coefficients (2019) - T. Lamm - A. Malchiodi - M. Micallef (Submitted Paper)

A gap theorem for $\alpha$-harmonic maps between two-spheres (2019) - H. Lavenant (Phd Thesis)

Optimal curves and mappings valued in the Wasserstein space (2019) - H. Lavenant (Preprint)

Unconditional convergence for discretizations of dynamical optimal transport (2019) - G. Lazzaroni - L. Nardini (Accepted Paper:
*ESAIM: COCV*)

On the 1d wave equation in time-dependent domains and the problem of debond initiation (2019) - E. Le Donne - S. Nicolussi Golo (preprint)

Metric Lie groups admitting dilations (2019) - H. Leclerc - Q. Mérigot - F. Santambrogio - F. Stra (Preprint)

Lagrangian discretization of crowd motion and linear diffusion (2019) - M. Lewicka - D. Lučić (Accepted Paper:
*Communications on Pure and Applied Mathematics*)

Dimension reduction for thin films with transversally varying prestrain: the oscillatory and the non-oscillatory case (2019) - P. Liu - X. Y. Lu (Submitted Paper)

Real order (an)-isotropic total variation in image processing - Part II: Learning of optimal structures (2019) - D. Wang - A. Rinaldo - X. Y. Lu (Submitted Paper)

DBSCAN: Optimal Rates For Density Based Clustering (2019) - L. Lussardi (To appear:
*Rend. Sem. Mat. Univ. Pol. Torino*)

The Plateau problem in the Calculus of Variations (2019) - D. Lučić - E. Pasqualetto - T. Rajala (Preprint)

Sharp estimate on the inner distance in planar domains (2019) - F. Maddalena - E. Mainini - D. Percivale (Preprint)

Euler's optimal profile problem (2019) - F. Maddalena - D. Percivale - F. Tomarelli

A new variational approach to linearization of traction problems in elasticity (2019) - F. Maddalena - D. Percivale - F. Tomarelli (Accepted Paper:
*Arch Rational Mech Anal (2019)*)

The Gap Between Linear Elasticity and the Variational Limit of Finite Elasticity in Pure Traction Problems (2019) - F. Maggi - A. Scardicchio - S. Stuvard (
*Discrete Cont. Dyn. Syst.*)

Soap films with gravity and almost-minimal surfaces (2019) - V. Magnani (
*Calc. Var. Partial Differential Equations*)

Towards a theory of area in homogeneous groups (2019) - V. Magnani - A. Minne (Submitted Paper)

Optimal Regularity of Solutions to No-Sign Obstacle-Type Problems for the Sub-Laplacian (2019) - A. Maione (preprint)

$H$-convergence for equations depending on monotone operators in Carnot groups (2019) - A. Maione - A. Pinamonti - F. Serra Cassano (Submitted Paper)

$\Gamma$-convergence for functionals depending on vector fields I. Integral representation and compactness. (2019) - C. Mantegazza - M. Novaga - A. Pluda (Lecture Notes:
*Springer INdAM Series*)

Lectures on Curvature Flow of Networks (2019) - A. Marchese - A. Massaccesi - R. Tione (
*SIAM J. Math. Anal*)

A multi-material transport problem and its convex relaxation via rectifiable G-currents (2019) - J. Matias - M. Morandotti - D. R. Owen - E. Zappale (Preprint)

Relaxation of non-local energies for structured deformations with applications to plasticity (2019) - M. Mayer (preprint)

None compactness versus critical points at infinity: an example (2019) - M. Mayer (Submitted Paper)

Prescribing Morse scalar curvatures: critical points at infinity (2019) - D. Mazzoleni - B. Pellacci - G. Verzini (Preprint)

Quantitative analysis of a singularly perturbed shape optimization problem in a polygon (2019) - A. C. G. Mennucci (
*International Journal of Mathematics and Mathematical Sciences*)

On Perimeters and Volumes of Fattened Sets (2019) - A. C. G. Mennucci (Lecture Notes)

Some examples of Riemannian metrics of curves (2019) - I. A. Minlend - A. Niang - E. H. A. Thiam (Accepted Paper:
*ESAIM : COCV*)

Multiply-periodic hypersurfaces with constant nonlocal mean curvature (2019) - O. Misiats - I. Topaloglu - D. Vasiliu (preprint)

Singular perturbation of an elastic energy with a singular weight (2019) - S. Modena - G. Sattig (preprint)

Convex integration solutions to the transport equation with full dimensional concentration (2019) - A. Mondino - C. Scharrer (Preprint)

Existence and Regularity of Spheres Minimising the Canham-Helfrich Energy (2019) - M. Morandotti - F. Solombrino (Preprint)

Mean-field analysis of multi-population dynamics with label switching (2019) - P. van Meurs - M. Morandotti (Accepted Paper:
*SIAM J. App. Math.*)

Discrete-to-continuum limits of particles with an annihilation rule (2019) - D. Mucci - A. Saracco (Submitted Paper)

The total intrinsic curvature of curves in Riemannian surfaces (2019) - D. Mucci - A. Saracco (Submitted Paper)

The weak Frenet frame of non-smooth curves with finite total curvature and absolute torsion (2019) - S. Mukherjee - Y. Sire (Submitted Paper)

Gradient potential estimates on the Heisenberg Group (2019) - A. E. Muñoz Flores - S. Nardulli (
*Geometriae Dedicata*)

Local Hölder continuity of the isoperimetric profile in complete noncompact Riemannian manifolds with bounded geometry (2019) - L. Nenna - B. Pass (Submitted Paper)

Variational problems involving unequal dimensional optimal transport (2019) - Q. H. Nguyen - C. P. Nguyen (Submitted Paper)

Pointwise gradient estimates for a class of singular quasilinear equation with measure data (2019) - A. Niang (
*Communications on Pure and Applied Analysis*)

Boundary regularity for a degenerate elliptic equation with mixed boundary conditions (2019) - M. Novaga - P. Pozzi (Submitted Paper)

A second order gradient flow of $p$-elastic planar networks (2019) - V. Pagliari (Submitted Paper)

Halfspaces minimise nonlocal perimeter: a proof via calibrations (2019) - E. Pasqualetto (Preprint)

Direct and inverse limits of normed modules (2019) - X. Pellet - L. Scardia - C. I. Zeppieri (Accepted Paper:
*SIAM J. Math. Anal.*)

Homogenization of high-contrast Mumford-Shah energies (2019) - M. Pozzetta (Accepted Paper:
*Journal of Convex Analysis*)

A varifold perspective on the $p$-elastic energy of planar sets (2019) - B. Raita - D. Spector (Preprint)

A Note on Estimates for Elliptic Systems with $L^1$ Data (2019) - R. Rios-Zertuche (preprint)

Weak KAM theory in higher-dimensional holonomic measure flows (2019) - Rishabh S. Gvalani - A. Schlichting (preprint)

Barriers of the McKean--Vlasov energy via a mountain pass theorem in the space of probability measures (2019) - F. Riva (Submitted Paper)

A continuous dependence result for a dynamic debonding model in dimension one (2019) - F. Riva (Submitted Paper)

On the approximation of quasistatic evolutions for the debonding of a thin film via vanishing inertia and viscosity (2019) - R. Rossi (Accepted Paper:
*Mathematical Models and Methods in the Applied Sciences*)

Visco-Energetic solutions to some rate-independent systems in damage, delamination, and plasticity (2019) - R. Rossi - U. Stefanelli - M. Thomas (Submitted Paper)

Rate-independent evolution of sets (2019) - A. Saracco - G. Saracco (Accepted Paper:
*Netw. Heterog. Media*)

A discrete districting plan (2019) - G. Saracco (Preprint)

A sufficient criterion to determine planar self-Cheeger sets (2019) - G. Scilla - F. Solombrino (
*J. Differential Equations*)

A variational approach to the quasistatic limit of viscous dynamic evolutions in finite dimension (2019) - G. Scilla - B. Stroffolini (Submitted Paper)

Relaxation of nonlinear elastic energies related to Orlicz-Sobolev nematic elastomers (2019) - D. Spector (preprint)

New Directions in Harmonic Analysis on $L^1$ (2019) - S. Stuvard (
*Calc. Var. Partial Differential Equations*)

Multiple valued Jacobi fields (2019) - L. Tamanini (Preprint)

From Harnack inequality to heat kernel estimates on metric measure spaces and applications (2019) - E. Tasso (Submitted Paper)

On the blow-up of GSBV functions under suitable geometric properties of the jump set (2019) - P. Tilli - D. Zucco (Submitted Paper)

Optimal partitioning of an interval and applications to Sturm-Liouville eigenvalues (2019) - B. Velichkov (Lecture Notes)

Regularity of the one-phase free boundaries (2019) - D. Zucco (Accepted Paper:
*Calc. Var. Partial Differential Equations*)

Dirichlet conditions in Poincaré-Sobolev inequalities: the sub-homogeneous case (2019) - A. Zuniga (
*Nonlinear Analysis*)

Continuity of minimizers to weighted least gradient problems (2019)