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Projects
- Quasistatic and Dynamic Evolution Problems in Plasticity and Fracture (Gianni Dal Maso)
- Anisotropic geometric variational problems: existence, regularity and uniqueness (Antonio De Rosa)
- Analytic Techniques for Geometric and Functional Inequalities (Nicola Fusco)
- Geometry of Metric Groups (Enrico Le Donne) > papers
- Everything You Always Wanted to Know About the JKO Scheme (Filippo Santambrogio)
- Variational approach to the regularity of the free boundaries (Bozhidar Velichkov)
Open Positions
- 4 post-doc positions at the Scuola Superiore Meridionale (deadline: 15 Oct 2024)
- PhD Position at Goethe-University Frankfurt (deadline: 31 Oct 2024)
- Doctoral and postdoctoral positions at Mathematics Münster (deadline: 1 Nov 2024)
- ERC Postdoc position in sub-Riemannian geometry at SISSA, Trieste (Italy) (deadline: 6 Nov 2024)
- PhD position in differential geometry Frankfurt (deadline: 15 Nov 2024)
- 6 year research position in Lisbon (deadline: 29 Nov 2024)
- 2 ERC Postdoc positions at Bocconi University, Milan (deadline: 30 Nov 2024)
- Assistant Professor at Bocconi University (deadline: 15 Dec 2024)
- Expression of interest for a two-year postdoctoral position in Padova (Italy) (deadline: 31 Dec 2024)
Forthcoming Seminars
- 23 Oct 2024: M. J. Gursky: Some rigidity results for asymptotically hyperbolic Einstein metrics
Forthcoming Events
- 14 - 18 Oct 2024: Mathematical Materials Science: Defects and Polycrystals ICMS, Edinburgh
- 23 - 25 Oct 2024: Nonlinear partial differential equations in Salzburg Salzburg, Austria
- 28 - 29 Oct 2024: PDEs in Milan 2024 University of Milan
- 28 - 31 Oct 2024: Fall School "Boundary Analysis for Dispersive and Viscous Fluids" GSSI, L'Aquila, Italy
- 4 - 7 Nov 2024: conference "Spectral Theory and Differential Equations" University of Hradec Králové, Czech Republic
- 5 Nov - 5 Dec 2024: Γ-CONVERGENCE: A 50 YEARS LONG STORY Universitat de Barcelona
- 13 - 15 Nov 2024: PDE Festival@UniMi Università degli Studi di Milano, Room C11, Via Mangiagalli 25, Milano (Italy)
- 20 - 21 Nov 2024: Calculus of Variations and Free Boundary Problems IX Aula Magna, Dipartimento di Matematica, Università di Pisa
- 25 - 29 Nov 2024: Frontiers in Sub-Riemannian Geometry (Aux frontières de la géométrie sous-riemannienne) CIRM, Marseille (France)
- 26 - 28 Nov 2024: (Non)local (non)linear workshop I in Prague Prague, Czech Republic
- 28 - 29 Nov 2024: Workshop on Geometric properties and regularity in variational problems Pavia
- 2 - 6 Dec 2024: Optimal Transportation and Applications Centro di Ricerca Matematica Ennio De Giorgi, Pisa
- 18 - 20 Dec 2024: ASK Conference 2024 Università di Bologna, Italy
- 19 - 25 Jan 2025: Taiwan Winter School in Analysis Taipei
- 20 Jan - 7 Feb 2025: Calculus of Variations and PDE's in Geometric Analysis Sapienza, Università di Roma
- 10 - 14 Feb 2025: XXXIV Convegno Nazionale di Calcolo delle Variazioni Hotel Mediterraneo, Riccione
- 31 Mar - 4 Jul 2025: Intensive trimester at GSSI on "Particles, Fluids and Patterns: Analytical and Computational Challenges" Gran Sasso Science Institute, L'Aquila, Italy
- 1 - 7 Jun 2025: Spring School on Analysis 2025: Function Spaces and Applications XIII Paseky nad Jizerou, Czech Republic
- 16 - 20 Jun 2025: Vito Volterra Meeting in Calculus of Variations 2025
- 23 - 27 Jun 2025: Topics in Geometric Analysis Università di Pisa
- 23 - 27 Jun 2025: Workshop: Novel methods of PDEs and function spaces University of Warsaw
- 30 Jun - 4 Jul 2025: Topics in Geometric Measure Theory Università di Pisa
- 13 - 17 Jul 2025: Warsaw Summer School on Evolutionary PDEs University of Warsaw
- 9 - 13 Sep 2025: Diffusion in Warsaw 2025
Recently Added Papers
- S. Borza - M. Magnabosco - T. Rossi - K. Tashiro (preprint)
The curvature exponent of sub-Finsler Heisenberg groups (2024) - G. Bevilacqua - L. Lussardi - A. Marzocchi (preprint)
Soap films: from the Plateau problem to deformable boundaries (2024) - S. Eberle - A. Figalli - G. S. Weiss (Accepted Paper: Ann. of Math.)
Complete classification of global solutions to the obstacle problem (2024) - I. Fleschler - R. Resende (Preprint)
On the regularity of area minimizing currents at boundaries with arbitrary multiplicity (2024) - I. Fleschler (Preprint)
On the uniqueness of tangent cones to area minimizing currents at boundaries with arbitrary multiplicity (2024) - S. Honda - A. Mondino (Submitted Paper)
Gap phenomena under curvature restrictions (2024) - N. Gigli - S. Vincini (preprint)
Stability of the heat flow under convergence in concentration and consequences (2024) - M. Di Marco - A. Pinamonti - D. Vittone - K. Zambanini (Preprint)
Stepanov Differentiability Theorem for intrinsic graphs in Heisenberg groups (2024) - A. Figalli - J. P. G. Ramos (Submitted Paper)
Improved stability versions of the Prékopa–Leindler inequality (2024) - T. Schmidt - J. H. Schütt (Submitted Paper)
Partial regularity for variational integrals with Morrey-Hölder zero-order terms, and the limit exponent in Massari's regularity theorem (2024) - M. Cicalese - T. Heilmann (Preprint)
Surfactants in a non-local model for phase transitions (2024) - A. Guerra - X. Lamy - K. Zemas (Preprint)
On the existence of degenerate solutions of the two-dimensional H-system (2024) - G. Giovannardi - A. Pinamonti - S. Verzellesi (Preprint)
Curvature estimates for minimal hypersurfaces in the Heisenberg group (2024) - C. Alessi - L. Brasco - M. Miranda Jr (Preprint)
A Schroedinger operator with confining potential having quadratic growth (2024) - B. Han (Preprint)
ABP estimate on metric measure spaces via optimal transport (2024) - B. Han (Preprint)
Sharp and rigid isoperimetric inequality in metric measure spaces with non-negative Ricci curvature (2024) - B. Han (Journal of Functional Analysis)
On the asymptotic behaviour of the fractional Sobolev seminorms: a geometric approach (2024) - B. Han - Z. Xu (Calculus of Variations and Partial Differential Equations)
Sharp uncertainty principles on metric measure spaces (2024) - B. Han - D. Liu - Z. Zhu (Preprint)
On the geometry of Wasserstein barycenter I (2024) - N. Guglielmi - F. P. Maiale (Submitted Paper)
Gripenberg-like algorithm for the lower spectral radius (2024)
Recently Modified Papers
- M. Novaga - E. Paolini - V. M. Tortorelli (Accepted Paper: Trans. Amer. Math. Soc.)
Locally isoperimetric partitions (2023) - G. Bellettini - R. Marziani - R. Scala (Journal de l’École polytechnique — Mathématiques)
A non-parametric Plateau problem with partial free boundary (2024) - A. Braides - G. Dal Maso - C. Le Bris (Accepted Paper: Ann. Inst. H. Poincaré Anal. Non Linéaire)
A closure theorem for $\Gamma$-convergence and H-convergence with applications to non-periodic homogenization (2024) - E. G. Tolotti (preprint)
Stability of the Von Kármán regime for thin plates under Neumann boundary conditions (2024) - J. Candau-Tilh - M. Goldman - B. Merlet (Accepted Paper: Calc. Var. and PDEs)
An exterior optimal transport problem (2024) - P. Dondl - A. Maione - S. Wolff-Vorbeck (ESAIM: Control, Optimisation and Calculus of Variations)
Phase field model for multi-material shape optimization of inextensible rods (2024) - M. Santilli (IMRN)
Finite total curvature and soap bubbles with almost constant higher-order mean curvature (2024) - G. De Philippis - A. R. Mészáros - F. Santambrogio - B. Velichkov (Arch. Rat. Mech. Anal.)
BV Estimates in Optimal Transportation and Applications (2015) - D. Mazzoleni - G. Tortone - B. Velichkov (J. Convex Analysis: volume dedicated to Giuseppe Buttazzo on the occasion of his 70th birthday.)
On the dimension of the singular set in optimization problems with measure constraint (2024) - L. Ferreri - B. Velichkov (Accepted Paper: Trans. Amer. Math. Soc.)
Regularity for one-phase Bernoulli problems with discontinuous weights and applications (2023) - G. Buttazzo - M. van den Berg - B. Velichkov (Proceedings: Chapter in the book "New Trends in Shape Optimization")
Optimization problems involving the first Dirichlet eigenvalue and the torsional rigidity (2015) - M. Colombo - L. Spolaor - B. Velichkov (Geom. Funct. Anal.)
A logarithmic epiperimetric inequality for the obstacle problem (2018) - G. Buttazzo - B. Velichkov (SIAM J. Math. Anal.)
A Shape Optimal Control Problem with Changing Sign Data (2018) - D. Bucur - I. Fragalà - G. Verzini - B. Velichkov (Trans. Amer. Math. Soc.)
On the honeycomb conjecture for a class of minimal convex partitions (2018) - D. Mazzoleni - S. Terracini - B. Velichkov (Analysis & PDE)
Regularity of the free boundary for the vectorial Bernoulli problem (2020) - L. Spolaor - B. Velichkov (Comm. Pure Appl. Math.)
An epiperimetric inequality for the regularity of some free boundary problems: the $2$-dimensional case (2019) - M. Colombo - L. Spolaor - B. Velichkov (J. Reine Angew. Math.)
On the asymptotic behavior of the solutions to parabolic variational inequalities (2020) - M. Engelstein - L. Spolaor - B. Velichkov (Duke Math. J.)
Uniqueness of the blow-up at isolated singularities for the Alt-Caffarelli functional (2020) - M. Colombo - L. Spolaor - B. Velichkov (Comm. Pure Appl. Math.)
Direct epiperimetric inequalities for the thin obstacle problem and applications (2020) - L. Spolaor - B. Trey - B. Velichkov (Communications in Partial Differential Equations)
Free boundary regularity for a multiphase shape optimization problem (2018) - M. Engelstein - L. Spolaor - B. Velichkov (Geom. Topol.)
(Log-)epiperimetric inequality and regularity over smooth cones for almost Area-Minimizing currents (2019) - F. Générau - E. Oudet - B. Velichkov (ESAIM: M2AN)
Numerical computation of the cut locus via a variational approximation of the distance function (2022) - F. P. Maiale - G. Tortone - B. Velichkov (Annali della Scuola Normale Superiore di Pisa, Classe di Scienze)
The boundary Harnack principle on optimal domains (2024) - B. Velichkov (Lecture Notes: Lecture Notes of the Unione Matematica Italiana, Springer)
Regularity of the one-phase free boundaries (2020) - G. De Philippis - L. Spolaor - B. Velichkov (J. Eur. Math. Soc.)
(Quasi-)conformal methods in two-dimensional free boundary problems (2024) - G. Buttazzo - F. P. Maiale - B. Velichkov (Rend. Lincei Mat. Appl.)
Shape optimization problems in control form (2021) - F. P. Maiale - G. Tortone - B. Velichkov (Revista Matemática Iberoamericana)
Epsilon-regularity for the solutions of a free boundary system (2023) - M. Colombo - L. Spolaor - B. Velichkov (Interfaces and Free Boundaries)
Almost everywhere uniqueness of blow-up limits for the lower dimensional obstacle problem (2021) - N. Edelen - L. Spolaor - B. Velichkov (Indiana Univ. Math. J.)
A strong maximum principle for minimizers of the one-phase Bernoulli problem (2024) - F. Générau - E. Oudet - B. Velichkov (Arch. Rat. Mech. Anal.)
Cut locus on compact manifolds and uniform semiconcavity estimates for a variational inequality (2022) - N. Edelen - L. Spolaor - B. Velichkov (Calculus of Variations and Partial Differential Equations)
The symmetric (log-)epiperimetric inequality and a decay-growth estimate (2023) - T. Schmidt (Accepted Paper: Math. Ann.)
Isoperimetric conditions, lower semicontinuity, and existence results for perimeter functionals with measure data (2024) - G. P. Leonardi - G. Vianello (Accepted Paper: Transactions of the AMS)
A Vertex-Skipping property for almost-minimizers of the relative perimeter in convex sets (2024) - G. Carlier - A. Figalli - F. Santambrogio (Accepted Paper: Ann. Inst. H. Poincaré Anal. Non Linéaire)
On optimal transport maps between 1/d-concave densities (2024) - M. Datres - G. P. Leonardi - A. Figalli - D. Sutter (Accepted Paper: NeurIPS)
A Two-Scale Complexity Measure for Deep Learning Models (2024) - S. Di Marino - A. Gerolin - L. Nenna (Accepted Paper: Letters in Mathematical Physics)
Universal diagonal estimates for minimizers of the Levy-Lieb functional (2023) - F. Essebei - G. Giovannardi - S. Verzellesi (NoDEA Nonlinear Differential Equations Appl.)
Monge solutions for discontinuous Hamilton-Jacobi equations in Carnot groups (2024) - G. Giovannardi - A. Pinamonti - J. Pozuelo - S. Verzellesi (Adv. Math.)
The prescribed mean curvature equation for $t$-graphs in the Sub-Finsler Heisenberg group $\mathbb{H}^n$ (2024) - S. Almi - M. Caponi - M. Friedrich - F. Solombrino (Accepted Paper: Mathematische Annalen)
A fractional approach to strain-gradient plasticity: beyond core-radius of discrete dislocations (2024) - R. Marziani - F. Solombrino (Proceedings of the Royal Society Edinburgh Sect. A)
Non-local approximation of free-discontinuity problems in linear elasticity and application to stochastic homogenisation (2024) - F. Anceschi - G. Ascione - D. Castorina - F. Solombrino (Journal of Mathematical Analysis and Applications)
Well-posedness of Kolmogorov-Fokker-Planck equations with unbounded drift (2024) - F. Dragoni - Q. Liu - Y. Zhang (Preprint)
Horizontal semiconcavity for the square of Carnot-Carath\'eodory distance on step 2 Carnot groups and applications to Hamilton-Jacobi equations (2024) - G. Pascale - M. Pozzetta (Calculus of Variations and Partial Differential Equations)
Quantitative isoperimetric inequalities for classical capillarity problems (2024) - F. Lagoutière - F. Santambrogio - S. Tran Tien (Accepted Paper: Journal de l'Ecole Polytechnique - Mathématiques)
Vanishing viscosity limit for aggregation-diffusion equations (2024) - B. Han (Preprint)
Ricci tensor on smooth metric measure space with boundary (2017) - B. Han (Discrete and Continuous Dynamical Systems)
Self-improvement of gradient estimate of heat flows on metric measure spaces (2018) - N. Gigli - B. Han (Journal of Functional Analysis)
Sobolev Spaces on Warped Products (2018) - B. Han - K. T. Sturm (Annali di Matematica Pura ed Applicata)
Curvature-dimension conditions for diffusions under time change (2022) - B. Han (Manuscripta Mathematica)
The sharp $p$-Poincaré inequality under the measure contraction property (2020) - B. Han (Advances in Mathematics)
Measure rigidity of synthetic lower Ricci curvature bound on Riemannian manifolds (2020) - B. Han (Journal de Mathématiques Pures et Appliquées)
Rigidity of some functional inequalities on ${\rm RCD}$ spaces (2021) - B. Han (The Journal of Geometric Analysis)
Ricci tensor on ${\rm RCD}^*(K, N)$ spaces (2018) - B. Han (Potential Analysis)
Conformal transformation on metric measure spaces (2019) - B. Han - E. Milman (Ann. Sc. Norm. Super. Pisa Cl. Sci.)
Sharp Poincare inequality under Measure Contraction Property (2021) - B. Han (Calculus of Variations and Partial Differential Equations)
Characterizations of monotonicity of vector fields on metric measure space (2018) - N. Apollonio - D. De Canditiis - G. Franzina - P. Stolfi - G. L. Torrisi (Accepted Paper: Stochastic Systems)
Normal approximation of random Gaussian neural networks (2024) - A. Braides - E. Voglino - M. Zanardini (Netw. Heterogen. Media)
Microstructures and anti-phase boundaries in long-range lattice systems (2024)