Browsing by Author "Cabré Vilagut, Xavier"
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ADVANCED COURSE IN PARTIAL DIFFERENTIAL EQUATIONS
Cabré Vilagut, Xavier (Universitat Politècnica de Catalunya, 20180529)
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ADVANCED COURSE IN PARTIAL DIFFERENTIAL EQUATIONS
Cabré Vilagut, Xavier (Universitat Politècnica de Catalunya, 20170530)
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ADVANCED COURSE IN PARTIAL DIFFERENTIAL EQUATIONS
Cabré Vilagut, Xavier (Universitat Politècnica de Catalunya, 20170419)
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ADVANCED COURSE IN PARTIAL DIFFERENTIAL EQUATIONS
Cabré Vilagut, Xavier (Universitat Politècnica de Catalunya, 20180321)
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ADVANCED COURSE IN PARTIAL DIFFERENTIAL EQUATIONS
Cabré Vilagut, Xavier (Universitat Politècnica de Catalunya, 20160418)
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ADVANCED COURSE IN PARTIAL DIFFERENTIAL EQUATIONS
Cabré Vilagut, Xavier (Universitat Politècnica de Catalunya, 20160607)
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A gradient estimate for nonlocal minimal graphs
Cabré Vilagut, Xavier; Cozzi, Matteo (20190401)
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: onedimensional 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, 20191201)
Article
Restricted access  publisher's policyWe 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 ... 
An extension problem for sums of fractional Laplacians and 1D symmetry of phase transitions
Cabré Vilagut, Xavier; Serra Montolí, Joaquim (20150910)
Article
Open AccessWe study nonlinear elliptic equations for operators corresponding to nonstable Lévy diffusions. We include a sum of fractional Laplacians of different orders. Such operators are infinitesimal generators of nonstable ... 
Antisymmetry of solutions for some weighted elliptic problems
Cabré Vilagut, Xavier; Lucia, Marcello; Sanchón, Manel; Villegas, Salvador (20180317)
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 onedimensional case, we introduce the continuous ... 
A priori estimates for semistable solutions of semilinear elliptic equations
Cabré Vilagut, Xavier; Sanchón Rodellar, Manuel; Spruck, Joel (20160201)
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 C2 is a positive, nondecreasing, and convex nonlinearity ... 
Boundedness of stable solutions to semilinear elliptic equations: A survey
Cabré Vilagut, Xavier (20170501)
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 ... 
Curves and surfaces with constant nonlocal mean curvature: Meeting Alexandrov and Delaunay
Cabré Vilagut, Xavier; Fall, Mouhamed Moustapha; SolàMorales Rubió, Joan de (20181201)
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 (20170812)
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 ... 
Energy estimates and 1D symmetry for nonlinear equations involving the halfLaplacian
Cabré Vilagut, Xavier; Cinti, Eleonora (201011)
Article
Restricted access  publisher's policyWe establish sharp energy estimates for some solutions, such as global minimizers, monotone solutions and saddleshaped 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)
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EQUACIONS DE DERIVADES PARCIALS
Cabré Vilagut, Xavier (Universitat Politècnica de Catalunya, 20170704)
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EQUACIONS DE DERIVADES PARCIALS
Cabré Vilagut, Xavier (Universitat Politècnica de Catalunya, 20180528)
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EQUACIONS DE DERIVADES PARCIALS
Cabré Vilagut, Xavier (Universitat Politècnica de Catalunya, 20170609)
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