Exploració per autor "Cabré Vilagut, Xavier"
Ara es mostren els items 1-20 de 102
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A fractional Michael–Simon Sobolev inequality on convex hypersurfaces
Cabré Vilagut, Xavier; Cozzi, Matteo; Csató, Gyula (Elsevier, 2023-01-01)
Capítol de llibre / Carta nàutica
Accés obertThe classical Michael–Simon and Allard inequality is a Sobolev inequality for functions defined on a submanifold of Euclidean space. It is governed by a universal constant independent of the manifold, thanks to an additional ... -
A gradient estimate for nonlocal minimal graphs
Cabré Vilagut, Xavier; Cozzi, Matteo (2019-04-01)
Article
Accés obertWe consider the class of measurable functions defined in all of Rn that give rise to a nonlocal minimal graph over a ball of Rn. We establish that the gradient of any such function is bounded in the interior of the ball ... -
A mean field equation on a torus: one-dimensional symmetry of solutions
Cabré Vilagut, Xavier; Lucia D'Agostino, Marcello; Sanchón Rodellar, Manuel (2003)
Article
Accés obertWe study the equation $$-\Delta u=\lambda\left(\frac{e^u}{\int_\oep e^u}- \frac{1}{|\oep|}\right)\quad \text{in }\oep$$ for $u\in E$, where $E = \{ u \in H^1(\oep): u \hbox{ is doubly periodic}, \int_{\oep} u = 0 \}$ and ... -
A new proof of the boundedness results for stable solutions to semilinear elliptic equations
Cabré Vilagut, Xavier (American Institute of Mathematical Sciences, 2019-12-01)
Article
Accés obertWe consider the class of stable solutions to semilinear equations -¿u=f(u) in a bounded smooth domain of Rn. Since 2010 an interior a priori L8 bound for stable solutions is known to hold in dimensions n=4 for all C1 ... -
A priori estimates for semistable solutions of semilinear elliptic equations
Cabré Vilagut, Xavier; Sanchón Rodellar, Manuel; Spruck, Joel (2016-02-01)
Article
Accés obertWe consider positive semistable solutions u of Lu + f(u) = 0 with zero Dirichlet boundary condition, where L is a uniformly elliptic operator and f is an element of C-2 is a positive, nondecreasing, and convex nonlinearity ... -
A universal Hölder estimate up to dimension 4 for stable solutions to half-Laplacian semilinear equations
Cabré Vilagut, Xavier; Sanz Perela, Tomás (2022-04-25)
Article
Accés restringit per política de l'editorialWe study stable solutions to the equation , posed in a bounded domain of . For nonnegative convex nonlinearities, we prove that stable solutions are smooth in dimensions . This result, which was known only for , follows ... -
A Weierstrass extremal field theory for the fractional Laplacian
Cabré Vilagut, Xavier; Urtiaga Erneta, Iñigo; Felipe Navarro, Juan Carlos (De Gruyter, 2023-10-27)
Article
Accés restringit per política de l'editorialIn this paper, we extend, for the first time, part of the Weierstrass extremal field theory in the Calculus of Variations to a nonlocal framework. Our model case is the energy functional for the fractional Laplacian (the ... -
ADVANCED COURSE IN PARTIAL DIFFERENTIAL EQUATIONS
Cabré Vilagut, Xavier (Universitat Politècnica de Catalunya, 2017-05-30)
Examen
Accés restringit a la comunitat UPC -
ADVANCED COURSE IN PARTIAL DIFFERENTIAL EQUATIONS
Cabré Vilagut, Xavier (Universitat Politècnica de Catalunya, 2018-03-21)
Examen
Accés restringit a la comunitat UPC -
ADVANCED COURSE IN PARTIAL DIFFERENTIAL EQUATIONS
Cabré Vilagut, Xavier (Universitat Politècnica de Catalunya, 2016-04-18)
Examen
Accés restringit a la comunitat UPC -
ADVANCED COURSE IN PARTIAL DIFFERENTIAL EQUATIONS
Cabré Vilagut, Xavier (Universitat Politècnica de Catalunya, 2016-06-07)
Examen
Accés restringit a la comunitat UPC -
ADVANCED COURSE IN PARTIAL DIFFERENTIAL EQUATIONS
Cabré Vilagut, Xavier (Universitat Politècnica de Catalunya, 2017-04-19)
Examen
Accés restringit a la comunitat UPC -
ADVANCED COURSE IN PARTIAL DIFFERENTIAL EQUATIONS
Cabré Vilagut, Xavier (Universitat Politècnica de Catalunya, 2018-05-29)
Examen
Accés restringit a la comunitat UPC -
An extension problem for sums of fractional Laplacians and 1-D symmetry of phase transitions
Cabré Vilagut, Xavier; Serra Montolí, Joaquim (2015-09-10)
Article
Accés obertWe study nonlinear elliptic equations for operators corresponding to non-stable Lévy diffusions. We include a sum of fractional Laplacians of different orders. Such operators are infinitesimal generators of non-stable ... -
Antisymmetry of solutions for some weighted elliptic problems
Cabré Vilagut, Xavier; Lucia, Marcello; Sanchón, Manel; Villegas, Salvador (2018-03-17)
Article
Accés obertThis article concerns the antisymmetry, uniqueness, and monotonicity properties of solutions to some elliptic functionals involving weights and a double well potential. In the one-dimensional case, we introduce the continuous ... -
Boundedness of stable solutions to semilinear elliptic equations: A survey
Cabré Vilagut, Xavier (2017-05-01)
Article
Accés obertThis article is a survey on boundedness results for stable solutions to semilinear elliptic problems. For these solutions, we present the currently known L8 estimates that hold for all nonlinearities. Such estimates are ... -
Calibrations and null-Lagrangians for nonlocal perimeters and an application to the viscosity theory
Cabré Vilagut, Xavier (2020-02-04)
Article
Accés restringit per acord de confidencialitatFor nonnegative even kernels K, we consider the K-nonlocal perimeter functional acting on sets. Assuming the existence of a foliation of space made of solutions of the associated K-nonlocal mean curvature equation in an ... -
Curves and surfaces with constant nonlocal mean curvature: Meeting Alexandrov and Delaunay
Cabré Vilagut, Xavier; Fall, Mouhamed Moustapha; Solà-Morales Rubió, Joan de (2018-12-01)
Article
Accés obertWe are concerned with hypersurfaces of RN with constant nonlocal (or fractional) mean curvature. This is the equation associated to critical points of the fractional perimeter under a volume constraint. Our results are ... -
Delaunay hypersurfaces with constant nonlocal mean curvature
Cabré Vilagut, Xavier; Fall, Mouhamed Moustapha; Weth, Tobias (2017-08-12)
Article
Accés restringit per política de l'editorialWe study hypersurfaces of RN with constant nonlocal (or fractional) mean curvature. This is the equation associated with critical points of the fractional perimeter functional under a volume constraint. We establish the ... -
Discurs de l'honoris causa i elogi dels mèrits del professor Alessio Figalli, pel professor Xavier Cabré. 2019
Cabré Vilagut, Xavier (2019-11-22)
Imatge
Accés obert