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dc.contributor.authorCabré Vilagut, Xavier
dc.contributor.authorSanz Perela, Tomás
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.date.accessioned2023-06-07T10:13:32Z
dc.date.issued2022-04-25
dc.identifier.citationCabre, X.; Sanz, T. A universal Hölder estimate up to dimension 4 for stable solutions to half-Laplacian semilinear equations. "Journal of differential equations", 25 Abril 2022, vol. 317, p. 153-195.
dc.identifier.issn0022-0396
dc.identifier.otherhttps://arxiv.org/abs/2110.02245
dc.identifier.urihttp://hdl.handle.net/2117/388320
dc.description.abstractWe 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 from a new interior Hölder estimate that is completely independent of the nonlinearity f. A main ingredient in our proof is a new geometric form of the stability condition. It is still unknown for other fractions of the Laplacian and, surprisingly, it requires convexity of the nonlinearity. From it, we deduce higher order Sobolev estimates that allow us to extend the techniques developed by Cabré, Figalli, Ros-Oton, and Serra for the Laplacian. In this way we obtain, besides the Hölder bound for , a universal estimate in all dimensions. Our bound is expected to hold for , but this has been settled only in the radial case or when . For other fractions of the Laplacian, the expected optimal dimension for boundedness of stable solutions has been reached only when , even in the radial case.
dc.format.extent43 p.
dc.language.isoeng
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en derivades parcials
dc.subject.lcshDifferential equations, Partial
dc.subject.otherHalf-Laplacian
dc.subject.otherStable solutions
dc.subject.otherExtremal solution
dc.subject.otherInterior estimates
dc.subject.otherDirichlet problem
dc.titleA universal Hölder estimate up to dimension 4 for stable solutions to half-Laplacian semilinear equations
dc.typeArticle
dc.subject.lemacEquacions en derivades parcials
dc.contributor.groupUniversitat Politècnica de Catalunya. TF-EDP - Grup de Teoria de Funcions i Equacions en Derivades Parcials
dc.identifier.doi10.1016/j.jde.2022.02.001
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::35 Partial differential equations::35B Qualitative properties of solutions
dc.relation.publisherversionhttps://www.sciencedirect.com/science/article/abs/pii/S0022039622000870?via%3Dihub
dc.rights.accessRestricted access - publisher's policy
local.identifier.drac36603973
dc.description.versionPostprint (published version)
dc.relation.projectidinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-84214-C2-1-P/ES/ECUACIONES EN DERIVADAS PARCIALES: PROBLEMAS DE REACCION-DIFUSION, INTEGRO-DIFERENCIALES Y GEOMETRICOS/
dc.date.lift2024-04-25
local.citation.authorCabre, X.; Sanz, T.
local.citation.publicationNameJournal of differential equations
local.citation.volume317
local.citation.startingPage153
local.citation.endingPage195


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