Full Professor and FIM Director,
ETH Zurich
Email: alessio.figalli AT math.ethz.ch
Home-page: https://people.math.ethz.ch/~afigalli/
Available papers (167):
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- M. Datres - G. P. Leonardi - A. Figalli - D. Sutter (preprint)
A Two-Scale Complexity Measure for Deep Learning Models (2024)
- A. Figalli - X. Ros-Oton - J. Serra (Accepted Paper: J. Amer. Math. Soc)
The singular set in the Stefan problem (2023)
- A. Figalli - C. Kehle (Accepted Paper: Discrete Contin. Dyn. Syst.)
On the prescribed negative Gauss curvature problem for graphs (2022)
- A. Figalli - Y. R. Y. Zhang (Accepted Paper: Comm. Pure Appl. Math.)
Uniform boundedness for finite Morse index solutions to supercritical semilinear elliptic equations (2022)
- A. Figalli - S. Kim - H. Shahgholian (Nonlinear Anal.)
Lipschitz Regularity in Vectorial Linear Transmission Problems (2022)
- A. Figalli - A. Belotto da Silva - A. Parusiński - L. Rifford (Invent. Math.)
Strong Sard Conjecture and regularity of singular minimizing geodesics for analytic sub-Riemannian structures in dimension 3 (2022)
- A. Figalli - Y. R. Y. Zhang (Duke Mathematical Journal)
Sharp gradient stability for the Sobolev inequality (2022)
- A. Figalli - D. Jerison (Ann. Sci. Éc. Norm. Supér.)
A sharp Freiman type estimate for semisums in two and three dimensional Euclidean spaces (2021)
- M. Bonforte - A. Figalli (Comm. Pure Appl. Math.)
Sharp Extinction Rates for Fast Diffusion Equations on Generic Bounded Domains (2021)
- A. Figalli - X. Fernández-Real (Lecture Notes: Preprint)
The continuous formulation of shallow neural networks as wasserstein-type gradient flows (2020)
- Y. R. Y. Zhang - A. Figalli (Comm. Pure Appl. Math.)
Strong stability for the Wulff inequality with a crystalline norm (2020)
- X. Ros-Oton - J. Serra - A. Figalli (Publ. Math. Inst. Hautes Études Sci.)
Generic regularity of free boundaries for the obstacle problem (2020)
- X. Cabré - A. Figalli - X. Ros-Oton - J. Serra (Acta Mathematica)
Stable solutions to semilinear elliptic equations are smooth up to dimension 9 (2020)
- G. Ciraolo - A. Figalli - A. Roncoroni (Geometric and Functional Analysis)
Symmetry results for critical anisotropic $p$-Laplacian equations in convex cones (2020)
- X. Fernández-Real - A. Figalli (Mathematics in Engineering)
On the obstacle problem for the 1D wave equation (2020)
- L. Caffarelli - F. Cagnetti - A. Figalli (Arch. Ration. Mech. Anal.)
Optimal Regularity and Structure of the Free Boundary for Minimizers in Cohesive zone models (2020)
- A. Figalli - F. Glaudo (Arch. Ration. Mech. Anal.)
On the sharp stability of critical points of the Sobolev inequality (2020)
- A. Figalli - J. Serra (Invent. Math.)
On stable solutions for boundary reactions: a De Giorgi-type result in dimension 4+1 (2020)
- D. Cordero-Erausquin - A. Figalli (Accepted Paper: Discrete Contin. Dyn. Syst.)
Regularity of monotone transport maps between unbounded domains (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)
- 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. Figalli - J. Serra (Accepted Paper: Invent. Math.)
On the fine structure of the free boundary for the classical obstacle problem (2019)
- A. Figalli - F. Maggi - C. Mooney (Accepted Paper: Camb. J. Math.)
The sharp quantitative Euclidean concentration inequality (2018)
- A. Figalli (Accepted Paper: Nonlinear Anal.)
On the Continuity of Center-Outward Distribution and Quantile Functions (2018)
- A. Figalli (Lecture Notes)
Free boundary regularity in obstacle problems (2018)
- M. Bonforte - A. Figalli - J. L. Vazquez (Accepted Paper: Calc. Var. Partial Differential Equations)
Sharp boundary behaviour of solutions to semilinear nonlocal elliptic equations (2018)
- A. Figalli (Lecture Notes)
On the Monge-Ampère equation (2018)
- G. Ciraolo - A. Figalli - F. Maggi - M. Novaga (J. Reine Angew. Math.)
Rigidity and sharp stability estimates for hypersurfaces with constant and almost-constant nonlocal mean curvature (2018)
- A. Figalli (Proceedings: Proceedings ICM 2018)
Regularity of interfaces in phase transitions via obstacle problems (2018)
- S. Chen - A. Figalli (Accepted Paper: J. Funct. Anal.)
Partial $W^{2,p}$ regularity for optimal transport maps (2017)
- A. Figalli - B. Krummel - X. Ros-Oton (Accepted Paper: J. Differential Equations)
On the regularity of the free boundary in the p-Laplacian obstacle problem (2017)
- M. Colombo - A. Figalli - Y. Jhaveri (Accepted Paper: Ann. Sc. Norm. Super. Pisa Cl. Sci.)
Lipschitz changes of variables between perturbations of log-concave measures (2017)
- G. Ciraolo - A. Figalli - F. Maggi (Accepted Paper: Int. Math. Res. Not. IMRN)
A quantitative analysis of metrics on $\mathbb R^n$ with almost constant positive scalar curvature, with applications to fast diffusion flows (2017)
- A. Figalli - D. Jerison (Accepted Paper: Adv. Math.)
Quantitative stability for the Brunn-Minkowski inequality (2017)
- B. Barrios - A. Figalli - X. Ros-Oton (Accepted Paper: Amer. J. Math.)
Global regularity for the free boundary in the obstacle problem for the fractional Laplacian (2017)
- L. Ambrosio - M. Colombo - A. Figalli (Accepted Paper: Duke Math. J.)
On the Lagrangian structure of transport equations: the Vlasov-Poisson system (2017)
- A. Figalli - M. J. Kang - J. Morales (Accepted Paper: Arch. Ration. Mech. Anal.)
Global well-posedness of the spatially homogeneous Kolmogorov-Vicsek model as a gradient flow (2017)
- A. Figalli - C. Mooney (Accepted Paper: Arch. Ration. Mech. Anal.)
An obstacle problem for conical deformations of thin elastic sheets (2017)
- B. Barrios - A. Figalli - X. Ros-Oton (Accepted Paper: Comm. Pure Appl. Math.)
Free boundary regularity in the parabolic fractional obstacle problem (2017)
- M. Bonforte - A. Figalli - J. L. Vazquez (Accepted Paper: Anal. PDE)
Sharp global estimates for local and nonlocal porous medium-type equations in bounded domains (2017)
- S. Chen - A. Figalli (Accepted Paper: J. Math. Pures Appl.)
Stability results on the smoothness of optimal transport maps with general costs (2016)
- E. Baer - A. Figalli (Accepted Paper: Discrete Contin. Dyn. Syst.)
Characterization of isoperimetric sets inside almost-convex cones (2016)
- M. Bonforte - A. Figalli - X. Ros-Oton (Accepted Paper: Comm. Pure Appl. Math.)
Infinite speed of propagation and regularity of solutions to the fractional porous medium equation in general domains (2016)
- A. Figalli (Accepted Paper: J. Diff. Geom.)
Regularity of codimension-1 minimizing currents under minimal assumptions on the integrand (2016)
- A. Figalli - D. Gomes - D. Marcon (Accepted Paper: Calc. Var. Partial Differential Equations)
Weak KAM Theory for a Weakly Coupled System of Hamilton-Jacobi Equations (2016)
- A. Figalli (Lecture Notes: Boll. Unione Mat. Ital.)
A transportation approach to universality in random matrix theory (2016)
- A. Figalli - D. Jerison (Accepted Paper: Chin. Ann. Math.)
Quantitative stability of the Brunn-Minkowski inequality for sets of equal volume (2016)
- A. Figalli - A. Guionnet (Accepted Paper: Acta Math.)
Universality in several-matrix models via approximate transport maps (2016)
- A. Figalli - R. Neumayer (Accepted Paper: J. Eur. Math. Soc. (JEMS))
Gradient stability for the Sobolev inequality: the case $p\geq 2$ (2016)
- A. Figalli - J. Palmer - A. Pelayo (Accepted Paper: Ann. Scuola Norm. Sup. Pisa Cl. Sci. )
Symplectic G-capacities and integrable systems (2016)
- J. A. Carrillo - A. Figalli - F. S. Patacchini (Accepted Paper: Ann. Inst. H. Poincaré Anal. Non Linéaire)
Geometry of minimizers for the interaction energy with mildly repulsive potentials (2016)
- M. Cozzi - A. Figalli (Lecture Notes: CIME Lecture Notes)
Regularity theory for local and nonlocal minimal surfaces: an overview (2016)
- G. De Philippis - A. Figalli (Accepted Paper: Nonlinear Anal.)
Rigidity and stability of Caffarelli's log-concave perturbation theorem (2016)
- A. Figalli - H. Shahgholian (Accepted Paper: Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci.)
An overview of unconstrained free boundary problems (2015)
- L. Ambrosio - H. Brezis - J. Bourgain - A. Figalli (Accepted Paper: Comm. Pure Appl. Math.)
$BMO$-type norms related to the perimeter of sets (2015)
- A. Figalli (Lecture notes: CIME Lecture Notes)
Global existence for the semigeostrophic equations via Sobolev estimates for Monge-Ampère (2015)
- F. Bekermam - A. Figalli - A. Guionnet (Accepted Paper: Comm. Math. Phys.)
Transport maps for $\beta$-matrix models and Universality (2015)
- L. Ambrosio - M. Colombo - A. Figalli (Accepted Paper: Arch. Ration. Mech. Anal.)
Existence and uniqueness of maximal regular flows for non-smooth vector fields (2015)
- A. Figalli - A. Pelayo (Accepted Paper: Adv. Geom.)
On the density function on moduli spaces of toric 4-manifolds (2015)
- A. Figalli - Y. Jhaveri - C. Mooney (Accepted Paper: J. Funct. Anal.)
Nonlinear bounds in Hölder spaces for the Monge-Ampère equation (2015)
- A. Figalli - H. Shahgholian (Accepted Paper: Arch. Ration. Mech. Anal.)
A general class of free boundary problems for fully nonlinear elliptic equations (2014)
- A. Figalli - H. Shahgholian (Accepted Paper: Ann. Mat. Pura Appl.)
A general class of free boundary problems for fully nonlinear parabolic equations (2014)
- A. Figalli (Proceedings ICM 2014)
Quantitative stability results for the Brunn-Minkowski inequality (2014)
- S. Dipierro - A. Figalli - E. Valdinoci (Accepted Paper: Comm. Partial Differential Equations)
Strongly nonlocal dislocation dynamics in crystals (2014)
- A. Figalli - D. Jerison (Accepted Paper: J. Eur. Math. Soc. (JEMS))
Quantitative stability for sumsets in $R^n$ (2014)
- G. Contreras - A. Figalli - L. Rifford (Accepted Paper: Invent. Math.)
Generic hyperbolicity of Aubry sets on surfaces (2014)
- A. Figalli (Accepted Paper: Colloquium De Giorgi 2013-2014)
Stability results for the Brunn-Minkowski inequality (2014)
- A. Figalli - N. Fusco - F. Maggi - V. Millot - M. Morini (Accepted Paper: Comm. Math. Phys.)
Isoperimetry and stability properties of balls with respect to nonlocal energies (2014)
- A. Figalli - T. Gallouët - L. Rifford (Accepted Paper: SIAM J. Math. Anal.)
On the convexity of injectivity domains on nonfocal manifolds (2014)
- G. De Philippis - A. Figalli (Springer INdAM series)
Partial regularity results in optimal transportation (2014)
- S. Chen - A. Figalli (Accepted Paper: Adv. Math.)
Boundary $\varepsilon$-regularity in optimal transportation (2014)
- A. Figalli - E. Valdinoci (Accepted Paper: J. Reine Angew. Math.)
Regularity and Bernstein-type results for nonlocal minimal surfaces (2014)
- G. De Philippis - A. Figalli (Accepted Paper: Differential Integral Equations)
A note on the dimension of the singular set in free interface problems (2014)
- G. De Philippis - A. Figalli (Accepted Paper: Bull. Amer. Math. Soc.)
The Monge-Ampère equation and its link to optimal transportation (2014)
- G. De Philippis - A. Figalli (Accepted Paper: Publ. Math. Inst. Hautes Études Sci.)
Partial Regularity for optimal transport maps (2014)
- A. Figalli - C. Klein - P. Markovich - C. Sparber (Accepted Paper: Comm. Pure Appl. Math.)
WKB analysis of Bohmian dynamics (2013)
- S. Dipierro - A. Figalli - G. Palatucci - E. Valdinoci (Discrete Contin. Dyn. Syst.)
Asymptotics of the $s$-perimeter as $s \searrow 0$ (2013)
- A. Figalli - Y. H. Kim - R. J. McCann (Accepted Paper: Arch. Ration. Mech. Anal.)
Hölder continuity and injectivity of optimal maps (2013)
- A. Figalli - D. Jerison (Accepted Paper: J. Funct. Anal.)
How to recognize convexity of a set from its marginals (2013)
- A. Figalli - Y. H. Kim - R. J. McCann (Accepted Paper: Methods Appl. Anal.)
On supporting hyperplanes to convex bodies (2013)
- A. Figalli - L. Rifford (Accepted Paper: Comm. Pure Appl. Math.)
Closing Aubry sets I (2013)
- G. De Philippis - A. Figalli (Accepted Paper: Trans. Amer. Math. Soc.)
Optimal regularity of the convex envelope (2013)
- M. Colombo - A. Figalli (Accepted Paper: Discrete Contin. Dyn. Syst.)
An excess-decay result for a class of degenerate elliptic equations (2013)
- A. Figalli - L. Rifford (Accepted Paper: Comm. Pure Appl. Math.)
Closing Aubry sets II (2013)
- G. De Philippis - A. Figalli (Accepted Paper: Arch. Ration. Mech. Anal.)
Higher integrability for minimizers of the Mumford-Shah functional (2013)
- M. Bonforte - A. Figalli (Accepted Paper: J. Differential Equations)
Total Variation Flow and Sign Fast Diffusion in one dimension (2012)
- C. Bjorland - L. Caffarelli - A. Figalli (Accepted Paper: Adv. Math.)
Non-Local Gradient Dependent Operators (2012)
- A. Figalli - F. Maggi (Accepted Paper: Calc. Var. Partial Differential Equations)
On the isoperimetric problem for radial log-convex densities (2012)
- A. Figalli (Proceedings of the 6ECM)
Stability in geometric and functional inequalities (2012)
- E. Carlen - A. Figalli (Accepted Paper: Duke Math. J.)
Stability for a GNS inequality and the Log-HLS inequality, with application to the critical mass Keller-Segel equation (2012)
- B. Barrios - A. Figalli - E. Valdinoci (Accepted Paper: Ann. Scuola Norm. Sup. Pisa Cl. Sci.)
Bootstrap regularity for integro-differential operators and its application to nonlocal minimal surfaces (2012)
- A. Figalli (Proceedings)
Sobolev regularity for the Monge-Ampère equation, with application to the semigeostrophic equations (2012)
- L. Ambrosio - A. Figalli - E. Runa (Accepted Paper: Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl.)
On sets of finite perimeter in Wiener spaces: reduced boundary and convergence to halfspaces (2012)
- A. Figalli - L. Rifford (Proceedings : Contemp. Math.)
Aubry sets, Hamilton-Jacobi equations, and the Mañé Conjecture (2012)
- M. Colombo - A. Figalli (Accepted Paper: J. Math. Pures Appl.)
Regularity results for very degenerate elliptic equations (2012)
- A. Figalli - F. Maggi - A. Pratelli (Ann. Inst. Henri Poincaré Probab. Stat.)
A Geometric Approach to Correlation Inequalities in the Plane (2012)
- A. Figalli - F. Maggi - A. Pratelli (Adv. Math.)
Sharp stability theorems for the anisotropic Sobolev and log-Sobolev inequalities on functions of bounded variation (2012)
- G. De Philippis - A. Figalli (Accepted Paper: SIAM J. Math. Anal.)
Sobolev regularity for Monge-Ampère type equations (2012)
- L. Ambrosio - M. Colombo - G. De Philippis - A. Figalli (Accepted Paper: Discrete Contin. Dyn. Syst.)
A global existence result for the semigeostrophic equations in three
dimensional convex domains (2012)
- G. De Philippis - A. Figalli - O. Savin (Accepted Paper: Math. Ann.)
A note on interior $W^{2,1+\varepsilon}$ estimates for the Monge-Ampere
equation (2012)
- G. De Philippis - A. Figalli (Accepted Paper: Anal. PDE)
Second order stability for the Monge-Ampere equation and strong Sobolev
convergence of optimal transport maps (2012)
- 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)
- 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. Slepčev (Accepted Paper: Nonlinear Anal.)
Confinement in nonlocal interaction equations (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)
- A. Figalli - Y. Ge (Accepted Paper: Adv. Calc. Var.)
Isoperimetric-type inequalities on constant curvature manifolds (2011)
- L. Caffarelli - A. Figalli (J. Reine Angew. Math.)
Regularity of solutions to the parabolic fractional obstacle problem (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 (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)
- 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 - Y. H. Kim - R. J. McCann (Accepted Paper: J. Econom. Theory)
When is multidimensional screening a convex program? (2010)
- J. A. Carrillo - M. Di Francesco - A. Figalli - T. Laurent - D. Slepčev (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)
- A. Figalli (Proceedings: Contemp. Math.)
Quantitative isoperimetric inequalities, with applications to the stability of liquid drops and crystals (2010)
- A. Figalli - F. Maggi - A. Pratelli (Invent. Math.)
A mass transportation approach to quantitative isoperimetric inequalities (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)
- A. Figalli
A new transportation distance between non-negative measures, with applications to gradients flows with Dirichlet boundary conditions (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 - 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 (Accepted Paper: Comm. Partial Differential Equations)
Regularity properties of optimal maps between nonconvex domains in the plane (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 (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 (Ann. Inst. H. Poincaré Anal. Non Linéaire)
A refined Brunn-Minkowski inequality for convex sets (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)
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