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E-mail xavier.cabre@upc.edu
Position ICREA Research Professor
Research interests Analysis & PDE
Group Analysis And Partial Differential Equations
Cabré, Xavier
Biosketch

PhD in Mathematics, adviser: Louis Nirenberg, Courant Institute, New York University, 1994. Kurt Friedrichs Prize, New York University, 1995. Member of the Institute for Advanced Study, Princeton, 1994-95. Habilitation à diriger des recherches, Université Pierre et Marie Curie-Paris VI, 1998. Harrington Faculty Fellow, The University of Texas at Austin, 2001-02. Tenure Associate Professor, The University of Texas at Austin, 2002-03. ICREA Research Professor since 2003 and Catedrático de Matemática Aplicada since 2008, at the Universitat Politècnica de Catalunya. Fellow of the American Mathematical Society, inaugural class, 2012. Editor of the Journal of the European Mathematical Society, 2014-2017. Plenary speaker at the 8th European Congress of Mathematics, 2021. Frontiers of Science Award, first edition, awarded by the Chinese government at “The inaugural International Congress of Basic Science (ICBS)”, Beijing, 2023, for the article “Stable solutions to semilinear elliptic equations are smooth up to dimension 9” published in “Acta Mathematica” 224 (2020), 187-252. Full member of the "Institut d'Estudis Catalans", Science and Technology section, 2025.

Personal webpage: https://web.mat.upc.edu/xavier.cabre

Other Research Interests
  • Elliptic and parabolic PDEs
  • Fractional diffusion equations
  • Calculus of Variations
  • Isoperimetric and Sobolev inequalities
Selected publications

Cabré X, Figalli A, Ros-Oton X & Serra J, Stable solutions to semilinear elliptic equations are smooth up to dimension 9, Acta Math. 224 (2020), 187-252.

Cabré X & Cozzi M, A gradient estimate for nonlocal minimal graphs, Duke Math. J. 168 (2019), 775-848.

Cabré X & Sire Y, Nonlinear equations for fractional Laplacians I: Regularity, maximum principles, and Hamiltonian estimates, Ann. Inst. H. Poincaré Anal. Non Linéaire 31 (2014), 23-53.

Cabré X, Regularity of minimizers of semilinear elliptic problems up to dimension 4, Comm. Pure Appl. Math. 63 (2010), 1362-1380.

Cabré X & Solà-Morales J, Layer solutions in a half-space for boundary reactions, Comm. Pure Appl. Math. 58 (2005), 1678-1732.

Ambrosio L & Cabré X, Entire solutions of semilinear elliptic equations in R3 and a conjecture of De Giorgi, J. Amer. Math. Soc. 13 (2000), 725-739.