Browsing by Author "Cabré Vilagut, Xavier"
Now showing items 1-20 of 86
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A gradient estimate for nonlocal minimal graphs
Cabré Vilagut, Xavier; Cozzi, Matteo (2019-04-01)
Article
Open AccessWe 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
Open AccessWe 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
Open AccessWe 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
Open AccessWe 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 ... -
ADVANCED COURSE IN PARTIAL DIFFERENTIAL EQUATIONS
Cabré Vilagut, Xavier (Universitat Politècnica de Catalunya, 2017-04-19)
Exam
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ADVANCED COURSE IN PARTIAL DIFFERENTIAL EQUATIONS
Cabré Vilagut, Xavier (Universitat Politècnica de Catalunya, 2016-06-07)
Exam
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ADVANCED COURSE IN PARTIAL DIFFERENTIAL EQUATIONS
Cabré Vilagut, Xavier (Universitat Politècnica de Catalunya, 2018-05-29)
Exam
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ADVANCED COURSE IN PARTIAL DIFFERENTIAL EQUATIONS
Cabré Vilagut, Xavier (Universitat Politècnica de Catalunya, 2016-04-18)
Exam
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ADVANCED COURSE IN PARTIAL DIFFERENTIAL EQUATIONS
Cabré Vilagut, Xavier (Universitat Politècnica de Catalunya, 2017-05-30)
Exam
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ADVANCED COURSE IN PARTIAL DIFFERENTIAL EQUATIONS
Cabré Vilagut, Xavier (Universitat Politècnica de Catalunya, 2018-03-21)
Exam
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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
Open AccessWe 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
Open AccessThis 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
Open AccessThis 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
Restricted access - confidentiality agreementFor 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
Open AccessWe 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
Restricted access - publisher's policyWe 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 ... -
EDPs: una equació de la calor demostra la conjectura de Poincaré
Cabré Vilagut, Xavier (2022-05-11)
Audiovisual
Open AccessCicle de Xerrades Panoràmiques sobre temes de recerca d'actualitat adreçades a estudiants i joves investigadors. -
Energy estimates and 1-D symmetry for nonlinear equations involving the half-Laplacian
Cabré Vilagut, Xavier; Cinti, Eleonora (2010-11)
Article
Restricted access - publisher's policyWe establish sharp energy estimates for some solutions, such as global minimizers, monotone solutions and saddle-shaped solutions, of the fractional nonlinear equation 1/2 in R n. Our energy estimates hold for every ... -
Entire solutions of semilinear elliptic equations in R<sup>3</sup> and a conjecture of De Giorgi
Ambrosio, Luigi; Cabré Vilagut, Xavier (1999)
Article
Open Access -
EQUACIONS DE DERIVADES PARCIALS
Cabré Vilagut, Xavier (Universitat Politècnica de Catalunya, 2017-07-04)
Exam
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