Singular boundary behaviour and large solutions for fractional elliptic equations

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dc.contributor.authorAbatangelo, Nicola
dc.contributor.authorGómez Castro, David
dc.contributor.authorVázquez, Juan Luis
dc.date.accessioned2023-06-22T12:33:18Z
dc.date.available2023-06-22T12:33:18Z
dc.date.issued2022-12-08
dc.descriptionCRUE-CSIC (Acuerdos Transformativos 2022)
dc.description.abstractWe perform a unified analysis for the boundary behaviour of solutions to nonlocal fractional equations posed in bounded domains. Based on previous findings for some models of the fractional Laplacian operator, we show how it strongly differs from the boundary behaviour of solutions to elliptic problems modelled upon the Laplace–Poisson equation with zero boundary data. In the classical case it is known that, at least in a suitable weak sense, solutions of the homogeneous Dirichlet problem with a forcing term tend to zero at the boundary. Limits of these solutions then produce solutions of some non-homogeneous Dirichlet problem as the interior data concentrate suitably to the boundary. Here, we show that, for equations driven by a wide class of nonlocal fractional operators, different blowup phenomena may occur at the boundary of the domain. We describe such explosive behaviours and obtain precise quantitative estimates depending on simple parameters of the nonlocal operators. Our unifying technique is based on a careful study of the inverse operator in terms of the corresponding Green function.
dc.description.departmentDepto. de Análisis Matemático y Matemática Aplicada
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.sponsorshipUnión Europea. Horizonte 2020
dc.description.sponsorshipMinisterio de Ciencia e Innovación (MICINN)
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/76047
dc.identifier.doi10.1112/jlms.12692
dc.identifier.issn0024-6107
dc.identifier.officialurlhttps://doi.org/10.1112/jlms.12692
dc.identifier.urihttps://hdl.handle.net/20.500.14352/72818
dc.journal.titleJournal of the London Mathematical Society
dc.language.isoeng
dc.publisherWiley
dc.relation.projectIDNonlocal-CPD (883363)
dc.relation.projectIDPGC2018-098440-B-I00
dc.rightsAtribución 3.0 España
dc.rights.accessRightsopen access
dc.rights.urihttps://creativecommons.org/licenses/by/3.0/es/
dc.subject.ucmMatemáticas (Matemáticas)
dc.subject.unesco12 Matemáticas
dc.titleSingular boundary behaviour and large solutions for fractional elliptic equations
dc.typejournal article
dspace.entity.typePublication
relation.isAuthorOfPublicationfe4c14a6-9c7a-4ce9-a868-b42d84aada05
relation.isAuthorOfPublication.latestForDiscoveryfe4c14a6-9c7a-4ce9-a868-b42d84aada05
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