Show simple item record

dc.contributor.authorRos Oton, Xavier
dc.contributor.authorSerra Montolí, Joaquim
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
dc.date.accessioned2014-07-01T09:12:00Z
dc.date.available2014-07-01T09:12:00Z
dc.date.created2014-08-01
dc.date.issued2014-08-01
dc.identifier.citationRos, X.; Serra, J. The Pohozaev identity for the fractional Laplacian. "Archive for rational mechanics and analysis", 01 Agost 2014, vol. 213, núm. 2, p. 587-628.
dc.identifier.issn0003-9527
dc.identifier.urihttp://hdl.handle.net/2117/23348
dc.description.abstractIn this paper we prove the Pohozaev identity for the semilinear Dirichlet problem (-Delta)(s) u = f(u) in Omega, u equivalent to 0 in R-n\Omega. Here, s is an element of (0, 1), (-Delta)(s) is the fractional Laplacian in R-n, and Omega is a bounded C-1,C-1 domain. To establish the identity we use, among other things, that if u is a bounded solution then u/delta(s)vertical bar(Omega) is C-alpha up to the boundary partial derivative Omega, where delta(x) = dist(x, partial derivative Omega). In the fractional Pohozaev identity, the function u/delta(s)vertical bar(partial derivative Omega) plays the role that partial derivative u/partial derivative nu plays in the classical one. Surprisingly, from a nonlocal problem we obtain an identity with a boundary term (an integral over partial derivative Omega) which is completely local. As an application of our identity, we deduce the nonexistence of nontrivial solutions in star-shaped domains for supercritical nonlinearities.
dc.format.extent42 p.
dc.language.isoeng
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject.lcshPohozaev identity
dc.subject.lcshLaplace operator
dc.subject.lcshDirichlet problem
dc.subject.otherRegularity
dc.subject.otherEquations
dc.subject.otherBoundary
dc.titleThe Pohozaev identity for the fractional Laplacian
dc.typeArticle
dc.subject.lemacLaplacià
dc.subject.lemacDirichlet, Problema de
dc.identifier.doi10.1007/s00205-014-0740-2
dc.description.peerreviewedPeer Reviewed
dc.relation.publisherversionhttp://link.springer.com/article/10.1007%2Fs00205-014-0740-2
dc.rights.accessOpen Access
drac.iddocument14948248
dc.description.versionPreprint
upcommons.citation.authorRos, X.; Serra, J.
upcommons.citation.publishedtrue
upcommons.citation.publicationNameArchive for rational mechanics and analysis
upcommons.citation.volume213
upcommons.citation.number2
upcommons.citation.startingPage587
upcommons.citation.endingPage628


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record

All rights reserved. This work is protected by the corresponding intellectual and industrial property rights. Without prejudice to any existing legal exemptions, reproduction, distribution, public communication or transformation of this work are prohibited without permission of the copyright holder