[figalli]

Alessio Figalli

Full Professor, UT Austin

Email: figalli AT math.utexas.edu

Home-page: http://www.ma.utexas.edu/users/figalli/

Available papers (74):

• G. De Philippis - A. Figalli (Accepted Paper: Invent. Math.)
  $W^{2,1}$ regularity for solutions of the Monge-Ampère equation (2012)
• L. Ambrosio - M. Colombo - G. De Philippis - A. Figalli (Accepted Paper: Comm. Partial Differential Equations)
  Existence of Eulerian solutions to the semigeostrophic equations in physical space: the 2-dimensional periodic case (2012)
• M. Bonforte - A. Figalli (Accepted Paper: J. Differential Equations)
  Total Variation Flow and Sign Fast Diffusion in one dimension (2012)
• A. Figalli - F. Maggi (Preprint)
  On the isoperimetric problem for radial log-convex densities (2012)
• G. De Philippis - A. Figalli - O. Savin (Preprint)
  A note on interior $W^{2,1+ \varepsilon}$ estimates for the Monge-Ampère equation (2012)
• G. De Philippis - A. Figalli (Preprint)
  Second order stability for the Monge-Ampère equation and strong Sobolev convergence of optimal transport maps (2012)
• C. Bjorland - L. Caffarelli - A. Figalli (Accepted Paper: Adv. Math.)
  Non-Local Gradient Dependent Operators (2012)
• S. Dipierro - A. Figalli - G. Palatucci - E. Valdinoci (Submitted Paper)
  Asymptotics of the $s$-perimeter as $s \searrow 0$ (2012)
• G. De Philippis - A. Figalli (Submitted Paper)
  Optimal regularity of the convex envelope (2012)
• C. Bjorland - L. Caffarelli - A. Figalli (Accepted Paper: Comm. Pure Appl. Math.)
  Non-Local Tug-of-War and the Infinity Fractional Laplacian (2011)
• J. A. Carrillo - M. Di Francesco - A. Figalli - T. Laurent - D. Slepcev (Accepted Paper: Nonlinear Anal.)
  Confinement in nonlocal interaction equations (2011)
• A. Figalli - F. Maggi - A. Pratelli (Submitted Paper)
  Sharp stability theorems for the anisotropic Sobolev and log-Sobolev inequalities on functions of bounded variation (2011)
• A. Figalli - F. Maggi - A. Pratelli (Submitted Paper)
  A Geometric Approach to Correlation Inequalities in the Plane (2011)
• L. Ambrosio - A. Figalli - G. Friesecke - J. Giannoulis - T. Paul (Accepted Paper: Comm. Pure Appl. Math.)
  Semiclassical limit of quantum dynamics with rough potentials and well posedness of transport equations with measure initial data (2011)
• A. Figalli - L. Rifford - C. Villani (Accepted Paper: Amer. J. Math.)
  Nearly round spheres look convex (2011)
• A. Figalli - L. Rifford - C. Villani (Accepted Paper: Tohoku Math. J.)
  Necessary and sufficient conditions for continuity of optimal transport maps on Riemannian manifolds (2011)
• A. Figalli - Y. H. Kim - R. J. McCann (Accepted Paper: J. Eur. Math. Soc. (JEMS))
  Regularity of optimal transport maps on multiple products of spheres (2011)
• A. Figalli - L. Rifford - C. Villani (Accepted Paper: Differential Geom. Appl.)
  Tangent cut loci on surfaces (2011)
• A. Figalli - M. Ligabò - T. Paul (Accepted Paper: Indiana Univ. Math. J.)
  Semiclassical limit for mixed states with singular and rough potentials (2011)
• L. Caffarelli - A. Figalli (J. Reine Angew. Math.)
  Regularity of solutions to the parabolic fractional obstacle problem (2011)
• A. Figalli - Y. Ge (Accepted Paper: Adv. Calc. Var.)
  Isoperimetric-type inequalities on constant curvature manifolds (2011)
• A. Figalli - E. Indrei (Accepted Paper: J. Geom. Anal.)
  A sharp stability result for the relative isoperimetric inequality inside convex cones (2011)
• A. Figalli - V. Mandorino (Accepted Paper: Discrete Contin. Dyn. Syst. Series A)
  Fine properties of minimizers of mechanical Lagrangians with Sobolev potentials (2011)
• S. Daneri - A. Figalli (Lecture Notes)
  Variational models for the incompressible Euler equations (2011)
• A. Figalli - F. Maggi - A. Pratelli (Accepted Paper: Invent. Math.)
  A mass transportation approach to quantitative isoperimetric inequalities (2010)
• A. Figalli - F. Maggi (Accepted Paper: Arch. Ration. Mech. Anal.)
  On the shape of liquid drops and crystals in the small mass regime (2010)
• L. Ambrosio - G. Crippa - A. Figalli - L. V. Spinolo (Proceedings: IMA Vol. Math. Appl., Springer)
  Existence and uniqueness results for the continuity equation and applications to the chromatography system (2010)
• A. Figalli - Y. H. Kim - R. J. McCann (Accepted Paper: J. Econom. Theory)
  When is multidimensional screening a convex program? (2010)
• L. Ambrosio - A. Figalli (Accepted Paper: Ann. Fac. Sci. Toulouse Math.)
  Surface measures and convergence of the Ornstein-Uhlenbeck semigroup in Wiener spaces (2010)
• A. Figalli (Proceedings: Contemporary Mathematics)
  Quantitative isoperimetric inequalities, with applications to the stability of liquid drops and crystals (2010)
• J. A. Carrillo - M. Di Francesco - A. Figalli - T. Laurent - D. Slepcev (Accepted Paper: Duke Math. J.)
  Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations (2010)
• L. Ambrosio - A. Figalli (Accepted Paper: C. R. Math. Acad. Sci. Paris)
  Almost everywhere well-posedness of continuity equations with measure initial data (2010)
• A. Figalli - Y. H. Kim (Accepted Paper: Discrete Contin. Dyn. Syst. Series A)
  Partial regularity of Brenier solutions of the Monge-Ampère equation (2010)
• A. Figalli - W. Gangbo - T. Yolcu (Accepted Paper: Ann. Scuola Norm. Sup. Pisa Cl. Sci.)
  A variational method for a class of parabolic PDEs (2010)
• A. Figalli - L. Rifford - C. Villani (Accepted Paper: Calc. Var. Partial Differential Equations)
  On the Ma-Trudinger-Wang curvature on surfaces (2010)
• L. Ambrosio - G. Crippa - A. Figalli - L. V. Spinolo (SIAM J. Math. Anal.)
  Some new well-posedness results for continuity and transport equations, and applications to the chromatography system (2009)
• A. Figalli - N. Gigli (Accepted Paper: ESAIM Control Optim. Calc. Var.)
  Local semiconvexity of Kantorovich potentials on non-compact manifolds (2009)
• L. Ambrosio - A. Figalli (Lecture notes)
  Lecture notes on variational models for incompressible Euler equations (2009)
• A. Figalli - L. Rifford (Accepted Paper: Comm. Pure Appl. Math.)
  Continuity of optimal transport maps and convexity of injectivity domains on small deformations of S^2 (2009)
• A. Figalli - L. Rifford (Accepted Paper: Geom. Funct. Anal.)
  Mass Transportation on Sub-Riemannian Manifolds (2009)
• A. Figalli (Accepted Paper: Rend. Circ. Mat. Palermo)
  A note on the regularity of the free boundaries in the optimal partial transport problem (2009)
• A. Figalli (Accepted Paper: Comm. Partial Differential Equations)
  Regularity properties of optimal maps between nonconvex domains in the plane (2009)
• A. Figalli - N. Gigli (Accepted Paper: J. Math. Pures Appl.)
  A new transportation distance between non-negative measures, with applications to gradients flows with Dirichlet boundary conditions (2009)
• A. Figalli (S\'eminaire Bourbaki)
  Regularity of optimal transport maps (after Ma-Trudinger-Wang and Loeper) (2009)
• A. Figalli (Mémoire HDR)
  Optimal transport, Euler equations, Mather and DiPerna-Lions theories (2009)
• A. Figalli - F. Maggi - A. Pratelli (Accepted Paper: Ann. Inst. H. Poincaré Anal. Non Linéaire)
  A refined Brunn-Minkowski inequality for convex sets (2009)
• A. Figalli (Accepted Paper: Bull. Amer. Math. Soc.)
  Optimal transport. Old and new. [book review] (2009)
• L. Desvillettes - A. Figalli (Gazette SMF)
  Cédric Villani reçoit un prix de la Société Mathématique Européenne (2009)
• A. Figalli (Accepted Paper: Math. Ann.)
  On flows of $H^{3/2}$-vector fields on the circle (2009)
• A. Figalli - F. Maggi - A. Pratelli (Proc. Amer. Math. Soc.)
  A note on Cheeger sets (2008)
• A. Figalli (Accepted Paper: ESAIM Control Optim. Calc. Var.)
  A geometric lower bound on Grad's number (2008)
• A. Figalli - N. Juillet (Accepted Paper: J. Funct. Anal.)
  Absolute continuity of Wasserstein geodesics in the Heisenberg group (2008)
• A. Fathi - A. Figalli - L. Rifford (Accepted Paper: Comm. Pure Appl. Math.)
  On the Hausdorff Dimension of the Mather Quotient (2008)
• A. Figalli - C. Villani (Lecture Notes)
  Optimal Transport and Curvature (2008)
• A. Figalli - C. Villani (Accepted Paper: Methods Appl. Anal.)
  An approximation lemma about the cut locus, with applications in optimal transport theory (2008)
• A. Abbondandolo - A. Figalli (Accepted Paper: Journal of Fixed Point Theory and Applications)
  Invariant measures of Hamiltonian systems with prescribed asymptotic Maslov index (2008)
• M. Bernot - A. Figalli - F. Santambrogio (Accepted Paper: J. Math. Pures Appl.)
  Generalized solutions for the Euler equations in one and two dimensions (2008)
• A. Figalli - R. Philipowski (Accepted Paper: ALEA Lat. Am. J. Probab. Math. Stat.)
  Convergence to the viscous porous medium equation and propagation of chaos (2008)
• L. Ambrosio - A. Figalli (Accepted Paper: J. Funct. Anal.)
  On flows associated to Sobolev vector fields in Wiener spaces: an approach a' la DiPerna-Lions (2008)
• A. Figalli (Accepted Paper: Arch. Ration. Mech. Anal.)
  The optimal partial transport problem (2008)
• A. Figalli - G. Loeper (Accepted Paper: Calc. Var. Partial Differential Equations)
  $C^1$ regularity of solutions of the Monge-Ampère equation for optimal transport in dimension two (2008)
• A. Figalli (Ph.D. Thesis)
  Optimal transportation and action-minimizing measures (2007)
• A. Fathi - A. Figalli (Accepted Paper: Israel J. Math.)
  Optimal transportation on non-compact manifolds (2007)
• A. Figalli - C. Villani (Accepted Paper: Mathematische Zeitschrift)
  Strong displacement convexity on Riemannian manifolds (2007)
• A. Figalli (Accepted Paper: Proc. Amer. Math. Soc.)
  A simple proof of the Morse-Sard Theorem in Sobolev Spaces (2007)
• L. Ambrosio - A. Figalli (Accepted Paper: Calc. Var. Partial Differential Equations)
  On the regularity of the pressure field of Brenier's weak solutions to incompressible Euler equations (2007)
• A. Figalli (Accepted Paper: J. Funct. Anal.)
  Existence and uniqueness of martingale solutions for SDEs with rough or degenerate coefficients (2007)
• M. Bernot - A. Figalli (Accepted Paper: ESAIM: COCV)
  Synchronized traffic plans and stability of optima (2007)
• L. Ambrosio - A. Figalli (Accepted Paper: Arch. Rat. Mech. Anal.)
  Geodesics in the space of measure-preserving maps and plans (2007)
• A. Figalli (Accepted Paper: SIAM Journal on Mathematical Analysis)
  Existence, uniqueness and regularity of optimal transport maps (2006)
• A. Figalli (Degree Thesis (5th year))
  Trasporto ottimale su varietà non compatte (2006)
• A. Abbondandolo - A. Figalli (Accepted Paper: J. Differential Equations)
  High action orbits for Tonelli Lagrangians and superlinear Hamiltonians on compact configuration spaces (2006)
• A. Figalli (Accepted Paper: Rend. Sem. Mat. Univ. Padova)
  The Monge problem on non-compact manifolds (2006)
• A. Figalli (Degree Thesis (3rd year))
  Il problema di Bernstein e una congettura di De Giorgi (2004)