Exploració per autor "Cabré Vilagut, Xavier"
Ara es mostren els items 68-87 de 101
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Interior C<sup>2,a</sup> regularity theory for a class of nonconvex fully nonlinear elliptic equations
Cabré Vilagut, Xavier; Caffarelli, Luis A. (2001)
Article
Accés obertWe prove the interior C2,α regularity of solutions for some nonconvex fully nonlinear elliptic equations F(D2u, x) = f (x), x ∈ B1 ⊂ Rn. Our hypothesis is that, for every x ∈ B1, F(·,x) is the minimum of a concave operator ... -
Isoperimetric, Sobolev, and eigenvalue inequalities via the Alexandroff-Bakelman-Pucci method: A survey
Cabré Vilagut, Xavier (2017-01-05)
Article
Accés obertThis paper presents the proof of several inequalities by using the technique introduced by Alexandroff, Bakelman, and Pucci to establish their ABP estimate. First, the author gives a new and simple proof of a lower bound ... -
Layer solutions in a halfspace for boundary reactions
Cabré Vilagut, Xavier; Solà-Morales Rubió, Joan de (2005)
Article
Accés obert -
Near-sphere lattices with constant nonlocal mean curvature
Cabré Vilagut, Xavier; Fall, Mouhamed Moustapha; Weth, Tobias (2018-04)
Article
Accés obertWe are concerned with unbounded sets of RN whose boundary has constant nonlocal (or fractional) mean curvature, which we call CNMC sets. This is the equation associated to critical points of the fractional perimeter ... -
Nonlinear equations for fractional laplacians II: existence, uniqueness, and qualitative properties of solutions
Cabré Vilagut, Xavier; Sire, Yannick (2015-02-01)
Capítol de llibre
Accés obertThis paper, which is the follow-up to part I, concerns the equation (-Delta)(s)v + G'(v) = 0 in R-n, with s is an element of (0, 1), where (-Delta)(s) stands for the fractional Laplacian-the infinitesimal generator of a ... -
Nonlinear equations for fractional Laplacians, I: Regularity, maximum principles, and Hamiltonian estimates
Cabré Vilagut, Xavier; Sire, Yannick (2014-01-01)
Article
Accés restringit per política de l'editorialThis is the first of two articles dealing with the equation (-)sv = f (v) in Rn, with s ¿ (0,1), where (-)s stands for the fractional Laplacian — the in¿nitesimal generator of a Lévy process. This equation can be realized ... -
On a long-standing conjecture of E. De Giorgi: old and recent results
Alberti, Giovanni (1965- ); Ambrosio, Luigi; Cabré Vilagut, Xavier (2000)
Article
Accés obert -
On the stability of radial solutions of semilinear elliptic equations in all of R<sup>n</sup>
Cabré Vilagut, Xavier; Capella Kort, Antonio (2003)
Article
Accés obertWe establish that every nonconstant bounded radial solution u of −?u = f (u) in all of Rn is unstable if n ? 10. The result applies to every C1 nonlinearity f satisfying a generic nondegeneracy condition. In particular, ... -
Optimal regularity of stable solutions to nonlinear equations involving the p-Laplacian
Cabré Vilagut, Xavier; Miraglio, Pietro; Sanchón Rodellar, Manuel (2020-01-01)
Article
Accés obertWe consider the equation-¿pu=f(u)in a smooth bounded domain ofRn, where¿pis thep-Laplaceoperator. Explicit examples of unbounded stable energy solutions are known ifn=p+4pp-1. Instead, whenn<p+4pp-1, stable solutions have ... -
Positive solutions of nonlinear problems involving the square root of the Laplacian
Cabré Vilagut, Xavier; Tan, Jinggang (2009-05)
Report de recerca
Accés obertWe consider nonlinear elliptic problems involving a nonlocal operator: the square root of the Laplacian in a bounded domain with zero Dirichlet boundary conditions. For positive solutions to problems with power nonlinearities, ... -
Preface of Llavefest: A broad perspective on finite and infinite dimensional dynamical systems
Cabré Vilagut, Xavier; Delshams Valdés, Amadeu; Gidea, Marian; Zeng, Chongchun (American Institute of Mathematical Sciences, 2018-12-01)
Article
Accés obertWe prove that for any non-trivial perturbation depending on any two independent harmonics of a pendulum and a rotor there is global instability. The proof is based on the geometrical method and relies on the concrete ... -
Recent applications of Nirenberg’s classical ideas
Sormani, Christina; Cabré Vilagut, Xavier (2016-02-01)
Article
Accés obert -
Regularity of radial minimizers and extremal solutions of semilinear elliptic equations
Cabré Vilagut, Xavier; Capella Kort, Antonio (2005)
Article
Accés obertWe consider a special class of radial solutions of semilinear equations −?u = g(u) in the unit ball of Rn. It is the class of semi-stable solutions, which includes local minimizers, minimal solutions, and extremal ... -
Regularity of stable solutions to reaction-diffusion elliptic equations
Cabré Vilagut, Xavier (European Mathematical Society Press, 2023-07-14)
Capítol de llibre
Accés obertThe boundedness of stable solutions to semilinear (or reaction-diffusion) elliptic PDEs has been studied since the 1970s. In dimensions 10 and higher, there exist stable energy solutions which are unbounded (or singular). ... -
Regularity of stable solutions to semilinear elliptic equations
Cabré Vilagut, Xavier (2019-11-21)
Audiovisual
Accés obertThe regularity of stable solutions to semilinear elliptic PDEs has been studied since the 1970's. In dimensions 10 and higher, there exist singular stable energy solutions. In this talk I will describe a recent work with ... -
Round table
Figalli, Alessio; Vázquez, Juan Luís; Cabré Vilagut, Xavier; Serra, Joaquim; Bonforte, Matteo; Ros Oton, Xavier (2019-11-21)
Audiovisual
Accés obert -
Saddle-shaped solutions of bistable diffusion equations in all of R2m
Cabré Vilagut, Xavier; Mourao Terra, Joana (2009)
Article
Accés restringit per política de l'editorialWe study the existence and instability properties of saddle-shaped solutions of the semilinear elliptic equation 1u D f .u/ in the whole R2m, where f is of bistable type. It is known that in dimension 2m D 2 there ... -
Sharp energy estimates for nonlinear fractional diffusion equations
Cabré Vilagut, Xavier; Cinti, Eleonora (2014-01)
Article
Accés restringit per política de l'editorialWe study the nonlinear fractional equation (−Δ)su=f(u) in Rn, for all fractions 0<s<1 and all nonlinearities f . For every fractional power s∈(0,1) , we obtain sharp energy estimates for bounded global minimizers and for ... -
Sharp isoperimetric inequalities via the ABP
Cabré Vilagut, Xavier; Ros-Oton, Xavier; Serra, Joaquim (2016-01-01)
Article
Accés obertGiven an arbitrary convex cone of Rn, we find a geometric class of homogeneous weights for which balls centered at the origin and intersected with the cone are minimizers of the weighted isoperimetric problem in the convex ... -
Sobolev and isoperimetric inequalities with monomial weights
Cabré Vilagut, Xavier; Ros Oton, Xavier (2013)
Article
Accés restringit per política de l'editorialWe consider the monomial weight |x1|A1⋯|xn|An in Rn, where Ai⩾0 is a real number for each i=1,…,n, and establish Sobolev, isoperimetric, Morrey, and Trudinger inequalities involving this weight. They are the analogue of ...