Publications (77)
Regularity of optimal transport maps on multiple products of spheres
Alessio Figalli, Young-Heon Kim, Robert J. McCann
Lipschitz Changes of Variables between Perturbations of Log-concave Measures
Maria Colombo, Alessio Figalli, Yash Jhaveri
A note on the dimension of the singular set in free interface problems
Guido De Philippis, Alessio Figalli
Surface measures and convergence of the Ornstein-Uhlenbeck semigroup in Wiener spaces
Luigi Ambrosio, Alessio Figalli
Free boundary regularity in obstacle problems
Alessio Figalli
On the fine structure of the free boundary for the classical obstacle problem
Alessio Figalli, Joaquim Serra
Total Variation Flow and Sign Fast Diffusion in one dimension
Matteo Bonforte, Alessio Figalli
Invariant measures of Hamiltonian systems with prescribed asymptotic Maslov index
Alberto Abbondandolo, Alessio Figalli
Free boundary regularity in the parabolic fractional obstacle problem
Begoña Barrios, Alessio Figalli, Xavier Ros-Oton
On flows associated to Sobolev vector fields in Wiener spaces: an approach à la DiPerna-Lions
Luigi Ambrosio, Alessio Figalli
An overview of unconstrained free boundary problems
Alessio Figalli, Henrik Shahgholian
Almost everywhere well-posedness of continuity equations with measure initial data
Luigi Ambrosio, Alessio Figalli
A rigorous derivation from the kinetic Cucker-Smale model to the pressureless Euler system with nonlocal alignment
Alessio Figalli, Moon-Jin Kang
BMO-type norms related to the perimeter of sets
Luigi Ambrosio, Jean Bourgain, Haim Brezis +1
A global existence result for the semigeostrophic equations in three dimensional convex domains
Luigi Ambrosio, Maria Colombo, Guido De Philippis +1
On the density function on moduli spaces of toric 4-manifolds
Alessio Figalli, Ãlvaro Pelayo
Hölder continuity and injectivity of optimal maps
Alessio Figalli, Young-Heon Kim, Robert J. McCann
The sharp quantitative Euclidean concentration inequality
Alessio Figalli, Francesco Maggi, Connor Mooney
Sharp boundary behaviour of solutions to semilinear nonlocal elliptic equations
Matteo Bonforte, Alessio Figalli, Juan Luis Vazquez
Gradient stability for the Sobolev inequality: the case $p\geq 2$
Alessio Figalli, Robin Neumayer
Global well-posedness of the spatially homogeneous Kolmogorov-Vicsek model as a gradient flow
Alessio Figalli, Moon-Jin Kang, Javier Morales
On supporting hyperplanes to convex bodies
Alessio Figalli, Young-Heon Kim, Robert J. McCann
The Monge-Ampère equation and its link to optimal transportation
Guido De Philippis, Alessio Figalli
On the Lagrangian structure of transport equations: the Vlasov-Poisson system
Luigi Ambrosio, Maria Colombo, Alessio Figalli
Boundary $\varepsilon$-regularity in optimal transportation
Shibing Chen, Alessio Figalli
Non-Local Tug-of-War and the Infinity Fractional Laplacian
Clayton Bjorland, Luis Caffarelli, Alessio Figalli
On sets of finite perimeter in Wiener spaces: reduced boundary and convergence to halfspaces
Luigi Ambrosio, Alessio Figalli, Eris Runa
Regularity of interfaces in phase transitions via obstacle problems
Alessio Figalli
Universality in several-matrix models via approximate transport maps
Alessio Figalli, Alice Guionnet
On the Monge-Ampère equation
Alessio Figalli
Quantitative stability for sumsets in $R^n$
Alessio Figalli, David Jerison
On the Hausdorff Dimension of the Mather Quotient
Albert Fathi, Alessio Figalli, Ludovic Rifford
Global regularity for the free boundary in the obstacle problem for the fractional Laplacian
Begoña Barrios, Alessio Figalli, Xavier Ros-Oton
On the regularity of the free boundary in the $p$-Laplacian obstacle problem
Alessio Figalli, Brian Krummel, Xavier Ros-Oton
Rigidity and stability of Caffarelli's log-concave perturbation theorem
Guido De Philippis, Alessio Figalli
High action orbits for Tonelli Lagrangians and superlinear Hamiltonians on compact configuration spaces
Alberto Abbondandolo, Alessio Figalli
Symmetry results for critical anisotropic $p$-Laplacian equations in convex cones
Giulio Ciraolo, Alessio Figalli, Alberto Roncoroni
On the convexity of injectivity domains on nonfocal manifolds
Alessio Figalli, Thomas Gallouët, Ludovic Rifford
Semiclassical limit of quantum dynamics with rough potentials and well posedness of transport equations with measure initial data
Luigi Ambrosio, Alessio Figalli, Gero Friesecke +2
Infinite speed of propagation and regularity of solutions to the fractional porous medium equation in general domains
Matteo Bonforte, Alessio Figalli, Xavier Ros-Oton
Transport maps for Beta-matrix models and Universality
Florent Bekerman, Alessio Figalli, Alice Guionnet
Optimal transportation on non-compact manifolds
Albert Fathi, Alessio Figalli
Sobolev regularity for Monge-Ampère type equations
Guido De Philippis, Alessio Figalli
Partial Regularity for optimal transport maps
Guido De Philippis, Alessio Figalli
Higher integrability for minimizers of the Mumford-Shah functional
Guido De Philippis, Alessio Figalli
Regularity of monotone transport maps between unbounded domains
Dario Cordero-Erausquin, Alessio Figalli
Second order stability for the Monge-Ampere equation and strong Sobolev convergence of optimal transport maps
Guido De Philippis, Alessio Figalli
A general class of free boundary problems for fully nonlinear parabolic equations
Alessio Figalli, Henrik Shahgholian
Bootstrap regularity for integro-differential operators and its application to nonlocal minimal surfaces
Begoña Barrios Barrera, Alessio Figalli, Enrico Valdinoci
Characterization of isoperimetric sets inside almost-convex cones
Eric Baer, Alessio Figalli
Sharp Extinction Rates for Fast Diffusion Equations on Generic Bounded Domains
Matteo Bonforte, Alessio Figalli
Some new well-posedness results for continuity and transport equations, and applications to the chromatography system
Luigi Ambrosio, Gianluca Crippa, Alessio Figalli +1
How to recognize convexity of a set from its marginals
Alessio Figalli, David Jerison
Asymptotics of the $s$-perimeter as $s\searrow 0$
Serena Dipierro, Alessio Figalli, Giampiero Palatucci +1
Existence and uniqueness of maximal regular flows for non-smooth vector fields
Luigi Ambrosio, Maria Colombo, Alessio Figalli
A note on interior $W^{2,1+\varepsilon}$ estimates for the Monge-Ampere equation
Guido De philippis, Alessio Figalli, Ovidiu Savin
Regularity of solutions to the parabolic fractional obstacle problem
Luis Caffarelli, Alessio Figalli
Mass Transportation on Sub-Riemannian Manifolds
Alessio Figalli, Ludovic Rifford
Continuity and injectivity of optimal maps for non-negatively cross-curved costs
Alessio Figalli, Young-Heon Kim, Robert J. McCann
Symplectic $G$-capacities and integrable systems
Alessio Figalli, Joseph Palmer, Ãlvaro Pelayo
Strongly nonlocal dislocation dynamics in crystals
Serena Dipierro, Alessio Figalli, Enrico Valdinoci
Sharp global estimates for local and nonlocal porous medium-type equations in bounded domains
Matteo Bonforte, Alessio Figalli, Juan Luis Vazquez
On stable solutions for boundary reactions: a De Giorgi-type result in dimension 4+1
Alessio Figalli, Joaquim Serra
An obstacle problem for conical deformations of thin elastic sheets
Alessio Figalli, Connor Mooney
Regularity and Bernstein-type results for nonlocal minimal surfaces
Alessio Figalli, Enrico Valdinoci
A sharp stability result for the relative isoperimetric inequality inside convex cones
Alessio Figalli, Emanuel Indrei
Semiclassical limit for mixed states with singular and rough potentials
Alessio Figalli, Marilena Ligabo, Thierry Paul
When is multidimensional screening a convex program?
Alessio Figalli, Young-Heon Kim, Robert J. McCann
A quantitative analysis of metrics on $\mathbf{R}^n$ with almost constant positive scalar curvature, with applications to fast diffusion flows
Giulio Ciraolo, Alessio Figalli, Francesco Maggi
On the Continuity of Center-Outward Distribution and Quantile Functions
Alessio Figalli
Nonlinear Bounds in Hölder Spaces for the Monge-Ampère Equation
Alessio Figalli, Yash Jhaveri, Connor Mooney
Lecture notes on variational models for incompressible Euler equations
Luigi Ambrosio, Alessio Figalli
Partial $W^{2,p}$ regularity for optimal transport maps
Shibing Chen, Alessio Figalli
Existence of Eulerian solutions to the semigeostrophic equations in physical space: the 2-dimensional periodic case
Luigi Ambrosio, Maria Colombo, Guido De Philippis +1
Rigidity and sharp stability estimates for hypersurfaces with constant and almost-constant nonlocal mean curvature
Giulio Ciraolo, Alessio Figalli, Francesco Maggi +1
Quantitative stability for the Brunn-Minkowski inequality
Alessio Figalli, David Jerison
$W^{2,1}$ regularity for solutions of the Monge-Ampère equation
Guido De Philippis, Alessio Figalli