Browsing by Author "Cabré Vilagut, Xavier"
Now showing items 1-20 of 98
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A fractional Michael–Simon Sobolev inequality on convex hypersurfaces
(Elsevier, 2023-01-01)
Part of book or chapter of book / Nautical chart
Open AccessThe 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
(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
(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
(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
(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 ... -
A universal Hölder estimate up to dimension 4 for stable solutions to half-Laplacian semilinear equations
(2022-04-25)
Article
Restricted access - publisher's policyWe 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 ... -
ADVANCED COURSE IN PARTIAL DIFFERENTIAL EQUATIONS
(Universitat Politècnica de Catalunya, 2017-05-30)
Exam
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ADVANCED COURSE IN PARTIAL DIFFERENTIAL EQUATIONS
(Universitat Politècnica de Catalunya, 2017-04-19)
Exam
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ADVANCED COURSE IN PARTIAL DIFFERENTIAL EQUATIONS
(Universitat Politècnica de Catalunya, 2018-05-29)
Exam
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ADVANCED COURSE IN PARTIAL DIFFERENTIAL EQUATIONS
(Universitat Politècnica de Catalunya, 2018-03-21)
Exam
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ADVANCED COURSE IN PARTIAL DIFFERENTIAL EQUATIONS
(Universitat Politècnica de Catalunya, 2016-06-07)
Exam
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ADVANCED COURSE IN PARTIAL DIFFERENTIAL EQUATIONS
(Universitat Politècnica de Catalunya, 2016-04-18)
Exam
Restricted access to the UPC academic community -
An extension problem for sums of fractional Laplacians and 1-D symmetry of phase transitions
(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
(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
(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
(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
(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
(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 ... -
Discurs de l'honoris causa i elogi dels mèrits del professor Alessio Figalli, pel professor Xavier Cabré. 2019
(2019-11-22)
Image
Open Access -
EDPs: una equació de la calor demostra la conjectura de Poincaré
(2022-05-11)
Audiovisual
Open AccessCicle de Xerrades Panoràmiques sobre temes de recerca d'actualitat adreçades a estudiants i joves investigadors.
