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dc.contributor.authorRos-Oton, Xavier
dc.contributor.authorSerra Montolí, Joaquim
dc.date.accessioned2017-05-22T08:13:27Z
dc.date.available2018-02-01T01:30:50Z
dc.date.issued2017-02-04
dc.identifier.citationRos-Oton, X., Serra, J. Boundary regularity estimates for nonlocal elliptic equations in C1 and C1, domains. "Annali di matematica pura ed applicata", 4 Febrer 2017, p. 1-32.
dc.identifier.issn0003-4622
dc.identifier.urihttp://hdl.handle.net/2117/104665
dc.description“The final publication is available at Springer via http://dx.doi.org/10.1007/s10231-016-0632-1"
dc.description.abstractWe establish sharp boundary regularity estimates in C1 and C1,a domains for nonlocal problems of the form Lu=f in O, u=0 in Oc. Here, L is a nonlocal elliptic operator of order 2s, with s¿(0,1). First, in C1,a domains we show that all solutions u are Cs up to the boundary and that u/ds¿Ca(O¯¯¯¯), where d is the distance to ¿O. In C1 domains, solutions are in general not comparable to ds, and we prove a boundary Harnack principle in such domains. Namely, we show that if u1 and u2 are positive solutions, then u1/u2 is bounded and Hölder continuous up to the boundary. Finally, we establish analogous results for nonlocal equations with bounded measurable coefficients in nondivergence form. All these regularity results will be essential tools in a forthcoming work on free boundary problems for nonlocal elliptic operators (Caffarelli et al., in Invent Math, to appear).
dc.format.extent32 p.
dc.language.isoeng
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals
dc.subject.lcshDifferential equations, Partial
dc.subject.lcshOperator theory
dc.subject.otherNonlocal equations
dc.subject.otherBoundary regularity
dc.subject.otherC1 domains
dc.titleBoundary regularity estimates for nonlocal elliptic equations in C1 and C1, domains
dc.typeArticle
dc.subject.lemacEquacions diferencials no lineals
dc.subject.lemacOperadors, Teoria dels
dc.contributor.groupUniversitat Politècnica de Catalunya. EDP - Equacions en Derivades Parcials i Aplicacions
dc.identifier.doi10.1007/s10231-016-0632-1
dc.description.peerreviewedPeer Reviewed
dc.relation.publisherversionhttp://link.springer.com/article/10.1007%2Fs10231-016-0632-1
dc.rights.accessOpen Access
local.identifier.drac19707853
dc.description.versionPostprint (published version)
local.citation.authorRos-Oton, X.; Serra, J.
local.citation.publicationNameAnnali di matematica pura ed applicata
local.citation.startingPage1
local.citation.endingPage32


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