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Mathematics

D-Index
37
Citations
7958
World Ranking
2448
National Ranking
43

Research.com Recognitions

  • 2013 - Fellow of the American Mathematical Society

Overview

Xavier Cabré is affiliated with the Universitat Politècnica de Catalunya in Spain. Their research spans multiple areas within mathematics and computer science, with a particular focus on applied mathematics and computational theory.

The main fields of study for Xavier Cabré include:

  • Mathematics
  • Computer Science

The subfields of study contributing to their work are:

  • Applied Mathematics
  • Computational Theory and Mathematics
  • Mathematical Physics
  • Numerical Analysis
  • Control and Systems Engineering

The research topics frequently covered involve:

  • Nonlinear Partial Differential Equations
  • Advanced Mathematical Modeling in Engineering
  • Geometric Analysis and Curvature Flows
  • Numerical methods in inverse problems
  • Differential Equations and Numerical Methods
  • Nonlinear Differential Equations Analysis
  • Advanced Harmonic Analysis Research

Notable recent publications by Xavier Cabré include:

  • The Bernstein Technique for Integro-Differential Equations, 2022, Archive for Rational Mechanics and Analysis
  • Calibrations and null-Lagrangians for nonlocal perimeters and an application to the viscosity theory, 2020, Annali di Matematica Pura ed Applicata (1923 -)
  • Universal Hardy-Sobolev inequalities on hypersurfaces of Euclidean space, 2021, Communications in Contemporary Mathematics
  • Optimal regularity of stable solutions to nonlinear equations involving the p-Laplacian, 2020, Advances in Calculus of Variations
  • Universal Hardy-Sobolev inequalities on hypersurfaces of Euclidean space, 2022, UPCommons (Polytechnic University of Catalonia)

Frequent co-authors collaborating with Xavier Cabré include:

  • Gyula Csató
  • Pietro Miraglio
  • Albert Mas Blesa
  • Iñigo U. Erneta
  • Juan-Carlos Felipe-Navarro

Common venues for their publications are:

  • arXiv (Cornell University)
  • Advances in Calculus of Variations
  • UPCommons (Polytechnic University of Catalonia)
  • Archive for Rational Mechanics and Analysis
  • Annali di Matematica Pura ed Applicata (1923 -)

Xavier Cabré was recognized as a Fellow of the American Mathematical Society in 2013.

Best Publications

  • Fully Nonlinear Elliptic Equations

    Luis A. Caffarelli;Xavier Cabré

  • Positive solutions of nonlinear problems involving the square root of the Laplacian

    Xavier Cabré;Jinggang Tan

  • Nonlinear equations for fractional Laplacians, I: Regularity, maximum principles, and Hamiltonian estimates

    Xavier Cabré;Yannick Sire

  • The parameterization method for invariant manifolds I: manifolds associated to non-resonant subspaces

    Xavier Cabre;Ernest Fontich;Rafael De La Llave

  • The parameterization method for invariant manifolds III: overview and applications

    Xavier Cabré;Ernest Fontich;Rafael de la Llave

  • Layer solutions in a half-space for boundary reactions

    Xavier Cabré;Joan Solà-Morales

  • Some simple nonlinear PDE's without solutions

    Haïm Brezis;Xavier Cabré

  • Nonlinear equations for fractional Laplacians II: Existence, uniqueness, and qualitative properties of solutions

    Xavier Cabré;Yannick Sire;Yannick Sire

  • On a long-standing conjecture of E. De Giorgi: symmetry in 3D for general nonlinearities and a local minimality property

    Giovanni Alberti;Luigi Ambrosio;Xavier Cabré

  • The parameterization method for invariant manifolds II: regularity with respect to parameters

    Xavier Cabre;Ernest Fontich;Rafael De La Llave

  • The Influence of Fractional Diffusion in Fisher-KPP Equations

    Xavier Cabré;Jean-Michel Roquejoffre

  • Existence versus explosion instantanée pour des équations de la chaleur linéaires avec potentiel singulier

    Xavier Cabré;Yvan Martel

  • On the alexandroff-bakelman-pucci estimate and the reversed hölder inequality for solutions of elliptic and parabolic equations

    Xavier Cabré

  • Regularity of radial minimizers and extremal solutions of semilinear elliptic equations

    Xavier Cabré;Xavier Cabré;Antonio Capella

  • ENERGY ESTIMATES AND 1-D SYMMETRY FOR NONLINEAR EQUATIONS INVOLVING THE HALF-LAPLACIAN

    Xavier Cabré;Eleonora Cinti

  • Sobolev and isoperimetric inequalities with monomial weights

    Xavier Cabré;Xavier Cabré;Xavier Ros-Oton

  • Regularity of minimizers of semilinear elliptic problems up to dimension 4

    Xavier Cabré

  • Sharp energy estimates for nonlinear fractional diffusion equations

    Xavier Cabré;Eleonora Cinti

  • Sharp isoperimetric inequalities via the ABP method

    Xavier Cabré;Xavier Ros-Oton;Joaquim Serra

  • Saddle-shaped solutions of bistable diffusion equations in all of ℝ2m

    Xavier Cabré;Joana Terra

  • Weak Eigenfunctions for the Linearization of Extremal Elliptic Problems

    Xavier Cabré;Yvan Martel

  • Regularity of minimizers of semilinear elliptic problems up to dimension four

    Xavier Cabre

Frequent Co-Authors

Tobias Weth
Tobias Weth Goethe University Frankfurt
Luis A. Caffarelli
Luis A. Caffarelli The University of Texas at Austin
Jean-Michel Roquejoffre
Jean-Michel Roquejoffre Toulouse Mathematics Institute
Rafael de la Llave
Rafael de la Llave Georgia Institute of Technology
Yvan Martel
Yvan Martel École Polytechnique
Luigi Ambrosio
Luigi Ambrosio National Research Council (CNR)
Joel Spruck
Joel Spruck Johns Hopkins University
Haim Brezis
Haim Brezis Rutgers, The State University of New Jersey

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