Xavier Cabré

Xavier Cabré Vilagut (born July 18, 1966 in Barcelona ) is a Spanish mathematician and professor at the Universitat Politècnica de Catalunya (UPC) in Barcelona. He deals with partial differential equations.

Cabré studied at the University of Barcelona with a bachelor's degree in 1989 and from 1990 at the Courant Institute at New York University , where he received his doctorate in 1994 under Louis Nirenberg ( Estimates for Solutions of Elliptic and Parabolic Equations ). He then worked at the Institute for Advanced Study until 1995 and then at what is now the Jacques-Louis Lions Laboratory at the University of Paris VI (Pierre et Marie Curie), where he completed his habilitation in 1998 (another habilitation followed in Spain in 2007). In 1998 he became Professor Titular at the UPC. From 2001 to 2002 he was a Harrington Faculty Fellow at the University of Texas at Austin , where he became an Associate Professor with tenure in 2002. In 2003 he became ICREA Research Professor and in 2008 Professor of Applied Mathematics at the UPC.

He was visiting professor at the University of Paris-Dauphine, the University of Cergy-Pontoise, the EHESS in Paris, in Toulouse, Rouen and the University of Chicago.

Cabré deals with partial differential equations , especially those of the elliptical and parabolic types. He makes use of geometric tools such as isoperimetric inequalities . He investigated reaction-diffusion equations, especially fractional diffusion, which are associated with jumps or Lévy processes . They are examples of the active research area of ​​anomalous diffusion.

In 1995 he received the Kurt Friedrichs Prize from New York University. In 2013 he became a Fellow of the American Mathematical Society . In 2020/21 he was selected as plenary speaker at the 8th ECM .

From 2014 to 2017 he was editor of the Journal of the European Mathematical Society.

Joaquim Serra is one of his PhD students .

Fonts (selection)

• with Luis Caffarelli : Fully nonlinear elliptic equations , AMS Colloquium Publ., 1995
• with Haïm Brezis : Some simple nonlinear PDE's without solutions , Bollettino della Unione Matematica Italiana 1-B, 1998, pp. 223-262
• with Luigi Ambrosio : Entire solutions of semilinear elliptic equations in and a conjecture of De Giorgi ${\displaystyle \mathbb {R} ^{3}}$ , Journal of the AMS, Volume 13, 2000, pp. 725-739
• with G. Alberti, L. Ambrosio: On a long-standing conjecture of E. De Giorgi: symmetry in 3D for general nonlinearities and a local minimality property , Acta Applicandae Mathematica, Volume 65, 2001, pp. 9-33
• with E. Fontich. R. de la Llave: The parameterization method for invariant manifolds I: manifolds associated to non-resonant subspaces , Indiana University Math. J., Volume 52, 2003, pp. 283–328, Part 2, Indiana University Math. J., Volume 52, 2003, pp. 329-360, Part 3, Journal of Differential Equations, Volume 218, 2005, pp. 444-515
• with J. Solà-Morales: Layer solutions in a half-space for boundary reactions , Communications on Pure and Applied Mathematics, Volume 58, 2005, pp. 1678-1732
• with J. Tan: Positive solutions of nonlinear problems involving the square root of the Laplacian , Advances in Mathematics, Volume 224, 2010, pp. 2052-2093
• mi Y. Sire: Nonlinear equations for fractional Laplacians, I: Regularity, maximum principles, and Hamiltonian estimates , Annales de l'Institut Henri Poincaré (Analyze non linéaire), Volume 31, 2014, pp. 23-53, Part 2, Transactions of the AMS, Volume 367, 2015, pp. 911-941

Web links

• Homepage, UPC

Individual evidence

1. ↑ Xavier Cabré in the Mathematics Genealogy Project (English)