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dc.contributor.author
Da Silva, Joao Vitor
dc.contributor.author
Salort, Ariel Martin
dc.date.available
2021-06-03T13:35:29Z
dc.date.issued
2019-07
dc.identifier.citation
Da Silva, Joao Vitor; Salort, Ariel Martin; A limiting obstacle type problem for the inhomogeneous p-fractional Laplacian; Springer; Calculus Of Variations And Partial Differential Equations; 58; 4; 7-2019; 1-30
dc.identifier.issn
0944-2669
dc.identifier.uri
http://hdl.handle.net/11336/133099
dc.description.abstract
In this manuscript we study an inhomogeneous obstacle type problem involving a fractional p-Laplacian type operator. First, we focus our attention in establishing existence and uniform estimates for any family of solutions {up}p≥2 which depend on the data of the problem and universal parameters. Next, we analyze the asymptotic behavior of such a family as p→ ∞. At this point, we prove that lim p → ∞up(x) = u∞(x) there exists (up to a subsequence), verifies a limiting obstacle type problem in the viscosity sense, and it is an s-Hölder continuous function. We also present several explicit examples, as well as further features of the limit solutions and their free boundaries. In order to establish our results we overcome several technical difficulties and develop new strategies, which were not present in the literature for this type of problems. Finally, we remark that our results are new even for problems governed by fractional p-Laplacian operator, as well as they extend the previous ones by dealing with more general non-local operators, source terms and boundary data.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Springer
dc.rights
info:eu-repo/semantics/restrictedAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
asymproric problems
dc.subject
obstacle problem
dc.subject.classification
Matemática Pura
dc.subject.classification
Matemáticas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
A limiting obstacle type problem for the inhomogeneous p-fractional Laplacian
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2020-11-18T17:30:28Z
dc.journal.volume
58
dc.journal.number
4
dc.journal.pagination
1-30
dc.journal.pais
Alemania
dc.journal.ciudad
Berlin
dc.description.fil
Fil: Da Silva, Joao Vitor. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Universidade do Brasília; Brasil. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
dc.description.fil
Fil: Salort, Ariel Martin. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
dc.journal.title
Calculus Of Variations And Partial Differential Equations
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/http://link.springer.com/10.1007/s00526-019-1573-5
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1007/s00526-019-1573-5
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