Local elliptic regularity for the Dirichlet fractional Laplacian

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dc.contributor.authorBiccari, Umberto
dc.contributor.authorWarma, Mahamadi
dc.contributor.authorZuazua, Enrique
dc.date.accessioned2025-01-07T13:57:30Z
dc.date.available2025-01-07T13:57:30Z
dc.date.issued2017
dc.date.updated2025-01-07T13:57:30Z
dc.description.abstractWe prove the Wloc2s,p local elliptic regularity of weak solutions to the Dirichlet problem associated with the fractional Laplacian on an arbitrary bounded open set of RN. The key tool consists in analyzing carefully the elliptic equation satisfied by the solution locally, after cut-off, to later employ sharp regularity results in the whole space. We do it by two different methods. First working directly in the variational formulation of the elliptic problem and then employing the heat kernel representation of solutions.en
dc.description.sponsorshipAll authorswere supported by the Air ForceOffice of Scientific Research through award no. FA9550-15-1-0027.Umberto Biccari and Enrique Zuazua were supported by Ministerio de Economía y Competitividad (Spain) through grant MTM2014-52347 and by the European Research Council Executive Agency through Advanced Grant DYCON (Dynamic Control). Enrique Zuazua was supported by EOARD-AFOSR through award no. FA9550-14-1-0214 and by Agence Nationale de la Recherche (France) through ICON.en
dc.identifier.citationBiccari, U., Warma, M., & Zuazua, E. (2017). Local Elliptic Regularity for the Dirichlet Fractional Laplacian. Advanced Nonlinear Studies, 17(2), 387-409. https://doi.org/10.1515/ANS-2017-0014
dc.identifier.doi10.1515/ANS-2017-0014
dc.identifier.issn1536-1365
dc.identifier.urihttp://hdl.handle.net/20.500.14454/2195
dc.language.isoeng
dc.publisherWalter de Gruyter GmbH
dc.rights© 2017 by De Gruyter
dc.subject.otherFractional Laplacian
dc.subject.otherDirichlet boundary condition
dc.subject.otherWeak solutions
dc.subject.otherLocal regularity
dc.titleLocal elliptic regularity for the Dirichlet fractional Laplacianen
dc.typejournal article
dcterms.accessRightsopen access
oaire.citation.endPage409
oaire.citation.issue2
oaire.citation.startPage387
oaire.citation.titleAdvanced Nonlinear Studies
oaire.citation.volume17
oaire.licenseConditionhttps://creativecommons.org/licenses/by-nc-nd/4.0/
oaire.versionVoR
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