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.accessioned2014-04-30T16:19:40Z
dc.date.created2014-03
dc.date.issued2014-03
dc.identifier.citationRos, X.; Serra, J. The Dirichlet problem for the fractional Laplacian: Regularity up to the boundary. "Journal de mathématiques pures et appliquées", Març 2014, vol. 101, núm. 3, p. 275-302.
dc.identifier.issn0021-7824
dc.identifier.urihttp://hdl.handle.net/2117/22795
dc.description.abstractWe study the regularity up to the boundary of solutions to the Dirichlet problem for the fractional Laplacian. We prove that if u is a solution of (-d)su=g in O, u=0 in Rn\O, for some s¿(0, 1) and g¿L8(O), then u is Cs(Rn) and u/ds|O is Ca up to the boundary ¿O for some a¿(0, 1), where d(x)=dist(x, ¿O). For this, we develop a fractional analog of the Krylov boundary Harnack method. Moreover, under further regularity assumptions on g we obtain higher order Hölder estimates for u and u/ds. Namely, the Cß norms of u and u/ds in the sets {x¿O:d(x)=¿} are controlled by C¿s-ß and C¿a-ß, respectively.These regularity results are crucial tools in our proof of the Pohozaev identity for the fractional Laplacian (Ros-Oton and Serra, 2012 [19,20]). © 2013 Elsevier Masson SAS.
dc.format.extent28 p.
dc.language.isoeng
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject.lcshBoundary element methods
dc.subject.lcshFractional Laplacian
dc.subject.otherBoundary regularity
dc.subject.otherDirichlet problem
dc.subject.otherFractional Laplacian
dc.titleThe Dirichlet problem for the fractional Laplacian: Regularity up to the boundary
dc.typeArticle
dc.identifier.doi10.1016/j.matpur.2013.06.003
dc.rights.accessRestricted access - publisher's policy
drac.iddocument13856130
dc.description.versionPostprint (published version)
dc.date.lift10000-01-01
upcommons.citation.authorRos, X.; Serra, J.
upcommons.citation.publishedtrue
upcommons.citation.publicationNameJournal de mathématiques pures et appliquées
upcommons.citation.volume101
upcommons.citation.number3
upcommons.citation.startingPage275
upcommons.citation.endingPage302


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record

Except where otherwise noted, content on this work is licensed under a Creative Commons license: Attribution-NonCommercial-NoDerivs 3.0 Spain