Alessio Figalli: magic, method, mission

DOI10.4171/NEWS/117/4zbMath1448.01031OpenAlexW3081538517MaRDI QIDQ2212848

Sebastian Xambó-Descamps

Publication date: 27 November 2020

Published in: European Mathematical Society Newsletter (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/news/117/4

Mathematics Subject Classification ID

Biographies, obituaries, personalia, bibliographies (01A70) History of calculus of variations and optimal control (49-03) History of partial differential equations (35-03)

Cites Work

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• The Monge-Ampère equation and its applications
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• On the regularity of solutions of optimal transportation problems
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• \(C^{1}\) regularity of solutions of the Monge-Ampère equation for optimal transport in dimension two
• The crystallization conjecture: a review
• The structure of branched transportation networks
• Scaling limits in statistical mechanics and microstructures in continuum mechanics
• A mass transportation approach to quantitative isoperimetric inequalities
• Functional analysis, Sobolev spaces and partial differential equations
• Existence and uniqueness of martingale solutions for SDEs with rough or degenerate coefficients
• The Wulff crystal in Ising and percolation models. École d'Été de Probabilités de Saint-Flour XXXIV -- 2004
• Minimal cones and the Bernstein problem
• Traffic plans
• Stable solutions to semilinear elliptic equations are smooth up to dimension \(9\)
• BMO-Type Norms Related to the Perimeter of Sets
• Nearly Round Spheres Look Convex
• Stability in geometric and functional inequalities
• Continuity of optimal transport maps and convexity of injectivity domains on small deformations of 𝕊²
• Entire solutions of semilinear elliptic equations in ℝ³ and a conjecture of De Giorgi
• Existence, Uniqueness, and Regularity of Optimal Transport Maps
• Book Review: Optimal transport: old and new
• Optimal Transport
• The Monge-Ampère equation
• On a long-standing conjecture of E. De Giorgi: symmetry in 3D for general nonlinearities and a local minimality property
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