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Alessio Figalli

  1. The Optimal Partial Transport Problem
    2009/01/20 by Alessio Figalli · 18 citations
    Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Point processes and geometric inequalities #Advanced Mathematical Modeling in Engineering
  2. Symmetry results for critical anisotropic p-Laplacian equations in\n convex cones
    2019/06/03 by Giulio Ciraolo, Ciraolo, Giulio, Alessio Figalli +3 · 12 citations
    Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Advanced Mathematical Modeling in Engineering
  3. Sharp gradient stability for the Sobolev inequality
    2020/03/09 by Alessio Figalli, Yi Ru‐Ya Zhang, Figalli, Alessio +1 · 11 citations
    Mathematics · #Nonlinear Partial Differential Equations
  4. Non-local gradient dependent operators
    2012/05/16 by C. Bjorland, Clayton Bjorland, L. Caffarelli +3 · 9 citations
    Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Geometric Analysis and Curvature Flows #Advanced Mathematical Modeling in Engineering
  5. On the fine structure of the free boundary for the classical obstacle\n problem
    2017/09/12 by Alessio Figalli, Figalli, Alessio, Joaquim Serra +1 · 4 citations
    Mathematics · #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds
  6. Mass Transportation on Sub-Riemannian Manifolds
    2008/03/20 by Alessio Figalli, Figalli, Alessio, Ludovic Rifford +1 · 3 citations
    Computer Science · Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Optimization and Control (math.OC) #Topological and Geometric Data Analysis
  7. The Cauchy-Dirichlet Problem for the Fast Diffusion Equation on Bounded Domains
    2023/08/16 by Matteo Bonforte, Bonforte, Matteo, Alessio Figalli +1 · 5 citations
    Computer Science · Mathematics · #35B40 #35J20 #35K55 #35K67 #35P30 #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations
  8. On flows associated to Sobolev vector fields in Wiener spaces: an approach à la DiPerna-Lions
    2008/03/10 by Luigi Ambrosio, Ambrosio, Luigi, Alessio Figalli +1 · 2 citations
    Economics, Econometrics and Finance · Mathematics · #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Dynamics and Fractals #Stochastic processes and financial applications #advanced mathematical theories
  9. Lecture notes on variational models for incompressible Euler equations
    2009/01/01 by Luigi Ambrosio, Alessio Figalli, Ambrosio, Luigi +1 · 2 citations
    Mathematics · #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations #Probability (math.PR)
  10. Semiclassical limit for mixed states with singular and rough potentials
    2010/12/11 by Alessio Figalli, Figalli, Alessio, Marilena Ligabò +3 · 2 citations
    Mathematics · #Spectral Theory in Mathematical Physics #Advanced Mathematical Physics Problems #Gas Dynamics and Kinetic Theory
  11. Infinite-width limit of deep linear neural networks
    2022/11/29 by Lénaïc Chizat, Chizat, Lénaïc, Maria Colombo +5 · 4 citations
    Computer Science · Mathematics · #35Q49 #68T07 #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Markov Chains and Monte Carlo Methods #Mathematical Approximation and Integration #Optimization and Control (math.OC) #Stochastic Gradient Optimization Techniques
  12. Partial W2,p regularity for optimal transport maps
    2016/06/16 by Shibing Chen, Chen, Shibing, Alessio Figalli +1 · 2 citations
    Mathematics · #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Point processes and geometric inequalities
  13. Sharp boundary behaviour of solutions to semilinear nonlocal elliptic\n equations
    2017/10/07 by Matteo Bonforte, Alessio Figalli, Bonforte, Matteo +2 · 2 citations
    Computer Science · Mathematics · #35B45 #35B65 #35J61 #35K67 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations
  14. Sharp quantitative stability of the Brunn-Minkowski inequality
    2023/10/31 by Alessio Figalli, Figalli, Alessio, Peter van Hintum +3 · 3 citations
    Computer Science · Mathematics · #49Q20 #52A27 #52A40 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Equations Stability Results #Metric Geometry (math.MG) #Point processes and geometric inequalities
  15. Stable solutions to semilinear elliptic equations are smooth up to\n dimension 9
    2019/07/22 by Xavier Cabré, Cabre, Xavier, Alessio Figalli +5 · 2 citations
    Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems
  16. Regularity of optimal transport maps on multiple products of spheres
    2010/06/10 by Alessio Figalli, Young‐Heon Kim, Figalli, Alessio +3 · 1 citation
    Mathematics · #35B65 #35J60 #49K20 #49N60 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations
  17. Universality in several-matrix models via approximate transport maps
    2014/07/10 by Alessio Figalli, Alice Guionnet, Figalli, Alessio +1 · 1 citation
    Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Random Matrices and Applications
  18. A quantitative analysis of metrics on Rn with almost constant positive scalar curvature, with applications to fast diffusion flows
    2016/02/05 by Giulio Ciraolo, Alessio Figalli, Ciraolo, Giulio +3 · 1 citation
    Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Metric Geometry (math.MG)
  19. Rigidity and sharp stability estimates for hypersurfaces with constant\n and almost-constant nonlocal mean curvature
    2015/03/02 by Giulio Ciraolo, Alessio Figalli, Ciraolo, Giulio +5 · 1 citation
    Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems
  20. Sharp stability of the Brunn-Minkowski inequality via optimal mass transportation
    2024/07/15 by Alessio Figalli, Peter van Hintum, Figalli, Alessio +3 · 3 citations
    Mathematics · #Point processes and geometric inequalities #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations
  21. Optimal regularity and structure of the free boundary for minimizers in\n cohesive zone models
    2017/12/21 by Luis Caffarelli, Caffarelli, Luis, Filippo Cagnetti +3 · 1 citation
    Computer Science · Engineering · Mathematics · #35B65 #35R35 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #Nonlinear Partial Differential Equations
  22. Sharp Quantitative Stability for the Prékopa-Leindler and Borell-Brascamp-Lieb Inequalities
    2025/01/08 by Alessio Figalli, Figalli, Alessio, Peter van Hintum +3 · 5 citations
    Mathematics · Physics and Astronomy · #26D15 #49Q20 #49Q22 #52A27 #52A40 #Analysis of PDEs (math.AP) #Combinatorics (math.CO) #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG) #Nonlinear Partial Differential Equations #Probability (math.PR) #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics
  23. Uniform boundedness for finite Morse index solutions to supercritical semilinear elliptic equations
    2021/06/21 by Alessio Figalli, Yi Ru‐Ya Zhang, Figalli, Alessio +1 · 1 citation
    Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems
  24. Serrin's overdetermined problem in rough domains
    2024/07/02 by Alessio Figalli, Figalli, Alessio, Yi Ru‐Ya Zhang +1 · 2 citations
    Computer Science · #35N25 #Analysis of PDEs (math.AP) #Computational Geometry and Mesh Generation #FOS: Mathematics
  25. Uniform boundedness for finite Morse index solutions to supercritical semilinear elliptic equations
    2023/07/21 by Alessio Figalli, Yi Ru‐Ya Zhang · 1 citation
    Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Advanced Mathematical Modeling in Engineering #Geometric Analysis and Curvature Flows
  26. Constraint maps with free boundaries: the Bernoulli case
    2023/11/06 by Alessio Figalli, Figalli, Alessio, André Guerra +5 · 1 citation
    Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations
  27. Constraint maps: singularities vs free boundaries
    2024/07/30 by Alessio Figalli, Figalli, Alessio, André Guerra +5 · 1 citation
    Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Homotopy and Cohomology in Algebraic Topology
  28. Sharp comparisons between sliced and standard 1-Wasserstein distances
    2025/10/18 by Guillaume Carlier, Alessio Figalli, Carlier, Guillaume +5 · 1 citation
    Mathematics · #39B62 #49Q22 #Commutative Algebra and Its Applications #FOS: Mathematics #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG) #Optimization and Control (math.OC) #Point processes and geometric inequalities #Statistics Theory (math.ST)