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Boundary regularity estimates for nonlocal elliptic equations in C1 and C1, domains
dc.contributor.author | Ros-Oton, Xavier |
dc.contributor.author | Serra Montolí, Joaquim |
dc.date.accessioned | 2017-05-22T08:13:27Z |
dc.date.available | 2018-02-01T01:30:50Z |
dc.date.issued | 2017-02-04 |
dc.identifier.citation | Ros-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.issn | 0003-4622 |
dc.identifier.uri | http://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.abstract | We 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.extent | 32 p. |
dc.language.iso | eng |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals |
dc.subject.lcsh | Differential equations, Partial |
dc.subject.lcsh | Operator theory |
dc.subject.other | Nonlocal equations |
dc.subject.other | Boundary regularity |
dc.subject.other | C1 domains |
dc.title | Boundary regularity estimates for nonlocal elliptic equations in C1 and C1, domains |
dc.type | Article |
dc.subject.lemac | Equacions diferencials no lineals |
dc.subject.lemac | Operadors, Teoria dels |
dc.contributor.group | Universitat Politècnica de Catalunya. EDP - Equacions en Derivades Parcials i Aplicacions |
dc.identifier.doi | 10.1007/s10231-016-0632-1 |
dc.description.peerreviewed | Peer Reviewed |
dc.relation.publisherversion | http://link.springer.com/article/10.1007%2Fs10231-016-0632-1 |
dc.rights.access | Open Access |
local.identifier.drac | 19707853 |
dc.description.version | Postprint (published version) |
local.citation.author | Ros-Oton, X.; Serra, J. |
local.citation.publicationName | Annali di matematica pura ed applicata |
local.citation.startingPage | 1 |
local.citation.endingPage | 32 |
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