**2019**
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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) - A. Agrachev - D. Barilari - U. Boscain (Lecture Notes:
*Cambridge Studies in Advanced Mathematics*)

A Comprehensive Introduction to Sub-Riemannian Geometry (2019) - G. Albi - M. Bongini - F. Rossi - F. Solombrino (Accepted Paper:
*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) - 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 - S. Fagioli (Submitted Paper)

Nonlinear diffusion equations with degenerate fast-decay mobility by coordinate transformation (2019) - A. H. Ardila - L. Cely - M. Squassina (Accepted Paper:
*Asymptotic Anal.*)

Logarithmic Bose-Einstein condensates with harmonic potential (2019) - A. Bach - M. Cicalese - M. Ruf (preprint)

Random finite-difference discretizations of the Ambrosio-Tortorelli functional with optimal mesh size (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 (Submitted Paper)

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 - I. Beschastnyi - A. Lerario (Accepted Paper:
*Journal of Symplectic Geometry*)

Volume of small balls and sub-Riemannian curvature in 3D contact manifolds (2019) - D. Barilari - S. Ivanov (
*Calc. Var. PDE*)

A Bonnet-Myers type theorem for quaternionic contact structures (2019) - D. Bartolucci - C. Gui - Y. Hu - A. Jevnikar - W. Yang (Preprint)

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) - 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) - G. Bevilacqua - L. Lussardi - A. Marzocchi (Submitted Paper)

Dimensional reduction of the Kirchhoff-Plateau problem (2019) - U. Bindini (preprint)

Smoothing operators in multi-marginal Optimal Transport (2019) - M. Bonafini - M. Novaga - G. Orlandi (Submitted Paper)

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) - P. Bousquet - L. Brasco (Accepted Paper:
*Rev. Mat. Iberoam.*)

Lipschitz regularity for orthotropic functionals with nonstandard growth conditions (2019) - A. Braides - V. Chiadò Piat (
*Applicable Analysis*)

Homogenization of networks in domains with oscillating boundaries (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) - K. Bredies - S. Fanzon (Submitted Paper)

An optimal transport approach for solving dynamic inverse problems in spaces of measures (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 - M. Miranda Jr (Preprint)

Rough traces of functions of bounded variation 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) - 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) - 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) - 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 - M. Morini - M. Novaga - M. Ponsiglione (
*Anal. PDE*)

Generalized crystalline evolutions as limits of flows with smooth anisotropies (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) - E. Cinti - F. Colasuonno (preprint)

A nonlocal supercritical Neumann problem (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) - 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) - G. Crasta - V. De Cicco - A. Malusa (Preprint)

Pairings between bounded divergence-measure vector fields and BV functions (2019) - V. Crismale (Accepted Paper:
*Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl.*)

Density in $SBD$ and approximation of fracture energies (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 - U. Stefanelli (Accepted Paper:
*SIAM Journal on Mathematical Analysis*)

Dynamic perfect plasticity as convex minimization (2019) - C. De Filippis - G. Palatucci (
*J. Differential Equations*)

Hölder regularity for nonlocal double phase equations (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) - 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) - C. Debin - N. Gigli - E. Pasqualetto (Submitted Paper)

Quasi-continuous vector fields on $\sf RCD$ spaces (2019) - G. Del Nin (Preprint)

Some asymptotic results on the global shape of planar clusters (2019) - D. Di Donato (preprint)

Intrinsic Lipschitz graphs in Carnot groups of step 2 (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) - 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 (Submitted Paper)

Optimal controlled transports with free end times subject to import/export tariffs (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) - F. Farroni - N. Fusco - S. Guarino Lo Bianco - R. Schiattarella (Submitted Paper)

A formula for the anisotropic total variation of SBV functions (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) - 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) - 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) - B. Han (Preprint)

Measure rigidity of synthetic lower Ricci curvature bound on Riemannian manifolds (2019) - S. Kholmatov - P. Piovano (Submitted Paper)

A unified model for stress-driven rearrangement instabilities (2019) - L. Kreutz - P. Piovano (Submitted Paper)

Microscopic validation of a variational model of epitaxially strained crystalline films (2019) - T. Lamm - A. Malchiodi - M. Micallef (Submitted Paper)

A gap theorem for $\alpha$-harmonic maps between two-spheres (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) - 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) - L. Lussardi (To appear:
*Rend. Sem. Mat. Univ. Pol. Torino*)

The Plateau problem in the Calculus of Variations (2019) - F. Maddalena - E. Mainini - D. Percivale (Preprint)

Euler's optimal profile problem (2019) - A. Maione - A. Pinamonti - F. Serra Cassano (Submitted Paper)

$\Gamma$-convergence for functionals depending on vector fields I. Integral representation and compactness. (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) - S. Modena - G. Sattig (preprint)

Convex integration solutions to the transport equation with full dimensional concentration (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) - 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) - 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 (Preprint)

A varifold perspective on the $p$-elastic energy of planar sets (2019) - R. Rios-Zertuche (preprint)

Weak KAM theory in higher-dimensional holonomic measure flows (2019) - F. Riva (Submitted Paper)

A continuous dependence result for a dynamic debonding model in dimension one (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) - D. Spector (preprint)

New Directions in Harmonic Analysis on $L^1$ (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)