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List of works by Alessio Figalli

A General Class of Free Boundary Problems for Fully Nonlinear Elliptic Equations

scientific article published on 4 April 2014

A Quantitative Analysis of Metrics on $\mathbb{R}^n$ with Almost Constant Positive Scalar Curvature, with Applications to Fast Diffusion Flows

scientific article published on 5 May 2017

A Sharp Stability Result for the Relative Isoperimetric Inequality Inside Convex Cones

scientific article published on 20 October 2011

A general class of free boundary problems for fully nonlinear parabolic equations

scientific article published on 12 March 2014

A geometric approach to correlation inequalities in the plane

scientific article published in February 2014

A geometric lower bound on Grad's number

scientific article published on 26 April 2008

A global existence result for the semigeostrophic equations in three dimensional convex domains

scientific article published in 2014

A mass transportation approach to quantitative isoperimetric inequalities

A new transportation distance between non-negative measures, with applications to gradients flows with Dirichlet boundary conditions

scientific article published in August 2010

A note on Cheeger sets

scientific article published on 26 January 2009

A note on interior $$W^{2,1+ \varepsilon }$$ estimates for the Monge–Ampère equation

scientific article published on 28 December 2012

A note on the regularity of the free boundaries in the optimal partial transport problem

scientific article published on 18 July 2009

A refined Brunn–Minkowski inequality for convex sets

scientific article published in December 2009

A rigorous derivation from the kinetic Cucker–Smale model to the pressureless Euler system with nonlocal alignment

scientific article published in January 2019

A simple proof of the Morse-Sard theorem in Sobolev spaces

scientific article published on 23 May 2008

A transportation approach to universality in random matrix theory

scientific article published on 15 June 2016

Absolute continuity of Wasserstein geodesics in the Heisenberg group

scientific article published in July 2008

Almost everywhere well-posedness of continuity equations with measure initial data

scientific article published in March 2010

An Obstacle Problem for Conical Deformations of Thin Elastic Sheets

scientific article published on 11 November 2017

An excess-decay result for a class of degenerate elliptic equations

scientific article published in 2014

An overview of unconstrained free boundary problems

scientific article

Asymptotics of the $s$-perimeter as $s\searrow 0$

scientific article published in 2013

BMO-Type Norms Related to the Perimeter of Sets

scientific article published on 5 October 2015

Boundary ε-regularity in optimal transportation

scientific article published in March 2015

C 1 regularity of solutions of the Monge–Ampère equation for optimal transport in dimension two

scientific article published on 30 January 2009

Characterization of isoperimetric sets inside almost-convex cones

scientific article published in 2017

Closing Aubry Sets I

scientific article published on 7 March 2014

Closing Aubry Sets II

scientific article published on 6 March 2014

Confinement in nonlocal interaction equations

scientific article published in January 2012

Continuity of optimal transport maps and convexity of injectivity domains on small deformations of 𝕊 2

scientific article published in December 2009

Corrigendum: Semiclassical Limit of Quantum Dynamics with Rough Potentials and Well-Posedness of Transport Equations with Measure Initial Data

scientific article published on 29 January 2013

Existence and Uniqueness of Maximal Regular Flows for Non-smooth Vector Fields

scientific article published on 19 May 2015

Existence and uniqueness of martingale solutions for SDEs with rough or degenerate coefficients

scientific article published in January 2008

Existence of Eulerian Solutions to the Semigeostrophic Equations in Physical Space: The 2-Dimensional Periodic Case

scientific article published in January 2012

Existence, Uniqueness, and Regularity of Optimal Transport Maps

scientific article published in January 2007

Fine properties of minimizers of mechanical Lagrangians with Sobolev potentials

scientific article published in 2011

Free Boundary Regularity in the Parabolic Fractional Obstacle Problem

scientific article published on 7 March 2018

Generalized solutions for the Euler equations in one and two dimensions

scientific article published in February 2009

Generic hyperbolicity of Aubry sets on surfaces

Geodesics in the Space of Measure-Preserving Maps and Plans

scientific article published on 7 November 2008

Geometry of minimizers for the interaction energy with mildly repulsive potentials

scientific article published in October 2017

Global Existence for the Semigeostrophic Equations via Sobolev Estimates for Monge-Ampère

scientific article published in 2018

Global Well-posedness of the Spatially Homogeneous Kolmogorov–Vicsek Model as a Gradient Flow

scientific article published on 22 September 2017

Global regularity for the free boundary in the obstacle problem for the fractional Laplacian

scientific article published in 2018

Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations

scientific article published in February 2011

Gradient stability for the Sobolev inequality: the case $p\geq 2$

scientific article published on 3 October 2018

High action orbits for Tonelli Lagrangians and superlinear Hamiltonians on compact configuration spaces

scientific article published in March 2007

Higher Integrability for Minimizers of the Mumford–Shah Functional

scientific article published on 27 March 2014

How to recognize convexity of a set from its marginals

scientific article published in February 2014

Hölder Continuity and Injectivity of Optimal Maps

scientific article published on 14 June 2013

Infinite Speed of Propagation and Regularity of Solutions to the Fractional Porous Medium Equation in General Domains

scientific article published on 19 October 2016

Invariant measures of Hamiltonian systems with prescribed asymptotic Maslov index

scientific article published in April 2008

Isoperimetric-type inequalities on constant curvature manifolds

scientific article published in January 2012

Isoperimetry and Stability Properties of Balls with Respect to Nonlocal Energies

scientific article published on 14 December 2014

Lipschitz regularity in vectorial linear transmission problems

Local semiconvexity of Kantorovich potentials on non-compact manifolds

scientific article published on 31 March 2010

Mass Transportation on Sub-Riemannian Manifolds

scientific article published on 23 February 2010

NEARLY ROUND SPHERES LOOK CONVEX

scientific article published in 2012

Necessary and sufficient conditions for continuity of optimal transport maps on Riemannian manifolds

scientific article published in January 2011

Non-local gradient dependent operators

scientific article published in July 2012

Nonlinear bounds in Hölder spaces for the Monge–Ampère equation

scientific article published in May 2016

Nonlocal Tug-of-War and the Infinity Fractional Laplacian

scientific article published on 20 October 2011

On flows associated to Sobolev vector fields in Wiener spaces: An approach à la DiPerna–Lions

scientific article published in January 2009

On flows of H 3/2-vector fields on the circle

scientific article published on 11 September 2009

On sets of finite perimeter in Wiener spaces: reduced boundary and convergence to halfspaces

scientific article published in 2013

On the Convexity of Injectivity Domains on Nonfocal Manifolds

scientific article published in January 2015

On the Hausdorff dimension of the mather quotient

scientific article published in April 2009

On the Lagrangian structure of transport equations: The Vlasov–Poisson system

scientific article published in 2017

On the Ma–Trudinger–Wang curvature on surfaces

scientific article published on 9 February 2010

On the Shape of Liquid Drops and Crystals in the Small Mass Regime

scientific article published on 30 October 2010

On the continuity of center-outward distribution and quantile functions

scientific article published in December 2018

On the density function on moduli spaces of toric 4-manifolds

scientific article published in July 2016

On the fine structure of the free boundary for the classical obstacle problem

article published in 2018

On the isoperimetric problem for radial log-convex densities

scientific article published on 3 October 2012

On the regularity of the free boundary in the p-Laplacian obstacle problem

scientific article published in August 2017

On the regularity of the pressure field of Brenier’s weak solutions to incompressible Euler equations

scientific article published on 8 August 2007

Optimal Transport and Curvature

scientific article published in 2011

Optimal transportation on non-compact manifolds

scientific article published in January 2010

Partial Regularity Results in Optimal Transportation

scientific article published in 2014

Partial regularity for optimal transport maps

Partial regularity of Brenier solutions of the Monge-Ampère equation

scientific article published in 2010

Perimeter of sets and BMO-type norms

scientific article published in September 2014

Preface

Quantitative stability for sumsets in $\mathbb R^n$

scientific article published in 2015

Quantitative stability for the Brunn–Minkowski inequality

scientific article published in July 2017

Quantitative stability of the Brunn-Minkowski inequality for sets of equal volume

scientific article published in March 2017

Regularity Properties of Optimal Maps Between Nonconvex Domains in the Plane

scientific article published on 25 February 2010

Regularity Theory for Local and Nonlocal Minimal Surfaces: An Overview

scientific article published in 2017

Regularity and Bernstein-type results for nonlocal minimal surfaces

scientific article published in January 2017

Regularity of $\textrm{codimension-}1$ minimizing currents under minimal assumptions on the integrand

scientific article published in June 2017

Regularity of monotone transport maps between unbounded domains

scientific article published in 2019

Regularity of optimal transport maps on multiple products of spheres

scientific article published in 2013

Regularity of solutions to the parabolic fractional obstacle problem

scientific article published in January 2013

Regularity results for very degenerate elliptic equations

scientific article published in January 2014

Rigidity and sharp stability estimates for hypersurfaces with constant and almost-constant nonlocal mean curvature

scientific article published in August 2018

Rigidity and stability of Caffarelli’s log-concave perturbation theorem

scientific article published in May 2017

Second order stability for the Monge–Ampère equation and strong Sobolev convergence of optimal transport maps

scientific article published on 21 August 2013

Semiclassical limit for mixed states with singular and rough potentials

scientific article published in 2012

Semiclassical limit of quantum dynamics with rough potentials and well-posedness of transport equations with measure initial data

Sharp boundary behaviour of solutions to semilinear nonlocal elliptic equations

scientific article published on 12 March 2018

Sharp global estimates for local and nonlocal porous medium-type equations in bounded domains

scientific article published on 12 January 2018

Sharp stability theorems for the anisotropic Sobolev and log-Sobolev inequalities on functions of bounded variation

scientific article published in August 2013

Sobolev Regularity for Monge-Ampère Type Equations

scientific article published in January 2013

Sobolev Regularity for the Monge−Ampère Equation, With Application to the Semigeostrophic Equations

scientific article published in January 2014

Some New Well-Posedness Results for Continuity and Transport Equations, and Applications to the Chromatography System

scientific article published in January 2009

Stability for a GNS inequality and the Log-HLS inequality, with application to the critical mass Keller–Segel equation

Stability results on the smoothness of optimal transport maps with general costs

scientific article published in August 2016

Strong displacement convexity on Riemannian manifolds

scientific article published on 8 May 2007

Strongly Nonlocal Dislocation Dynamics in Crystals

scientific article published on 16 September 2014

Synchronized traffic plans and stability of optima

scientific article published on 30 January 2008

Tangent cut loci on surfaces

scientific article published in March 2011

The Monge–Ampère equation and its link to optimal transportation

The Optimal Partial Transport Problem

scientific article published on 21 January 2009

Total Variation Flow and Sign Fast Diffusion in one dimension

scientific article published in April 2012

Transport Maps for $${\beta}$$ β -Matrix Models and Universality

scientific article published on 12 May 2015

Universality in several-matrix models via approximate transport maps

W 2,1 regularity for solutions of the Monge–Ampère equation

WKB Analysis of Bohmian Dynamics

scientific article published on 18 October 2013

Weak KAM theory for a weakly coupled system of Hamilton–Jacobi equations

scientific article published on 22 June 2016

When is multidimensional screening a convex program?

scientific article published in March 2011

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