Three representations of the fractional p-Laplacian:semigroup, extension and Balakrishnan formulas

We introduce three representation formulas for the fractional p-Laplace operator in the whole range of parameters 0 < s < 1 and 1 < p < ∞. Note that for p ≠ 2 this a nonlinear operator. The first representation is based on a splitting procedure that combines a renormalized nonlinearity w...

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Detalles Bibliográficos
Autores: Del Teso Méndez, Félix, Gómez-Castro, D., Vázquez, Juan Luis
Tipo de recurso: artículo
Fecha de publicación:2021
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/4992
Acceso en línea:https://hdl.handle.net/20.500.14352/4992
Access Level:acceso abierto
Palabra clave:517
517.9
Fractional p-Laplacian
Bochner’s subordination
Semigroup formula
Extension problem
Balakrishnan’s formula
Spectral formulation
Análisis matemático
Ecuaciones diferenciales
1202 Análisis y Análisis Funcional
1202.07 Ecuaciones en Diferencias
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oai_identifier_str oai:docta.ucm.es:20.500.14352/4992
network_acronym_str ES
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repository_id_str
spelling Three representations of the fractional p-Laplacian:semigroup, extension and Balakrishnan formulasDel Teso Méndez, FélixGómez-Castro, D.Vázquez, Juan Luis517517.9Fractional p-LaplacianBochner’s subordinationSemigroup formulaExtension problemBalakrishnan’s formulaSpectral formulationAnálisis matemáticoEcuaciones diferenciales1202 Análisis y Análisis Funcional1202.07 Ecuaciones en DiferenciasWe introduce three representation formulas for the fractional p-Laplace operator in the whole range of parameters 0 < s < 1 and 1 < p < ∞. Note that for p ≠ 2 this a nonlinear operator. The first representation is based on a splitting procedure that combines a renormalized nonlinearity with the linear heat semigroup. The second adapts the nonlinearity to the Caffarelli-Silvestre linear extension technique. The third one is the corresponding nonlinear version of the Balakrishnan formula. We also discuss the correct choice of the constant of the fractional p-Laplace operator in order to have continuous dependence as p → 2 and s → 0+, 1−. A number of consequences and proposals are derived. Thus, we propose a natural spectral-type operator in domains, different from the standard restriction of the fractional p-Laplace operator acting on the whole space. We also propose numerical schemes, a new definition of the fractional p-Laplacian on manifolds, as well as alternative characterizations of the Ws, p(ℝn) seminorms.SprigerUniversidad Complutense de Madrid20212021-08-2320212021-08-23journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/4992reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/49922026-06-02T12:44:21Z
dc.title.none.fl_str_mv Three representations of the fractional p-Laplacian:semigroup, extension and Balakrishnan formulas
title Three representations of the fractional p-Laplacian:semigroup, extension and Balakrishnan formulas
spellingShingle Three representations of the fractional p-Laplacian:semigroup, extension and Balakrishnan formulas
Del Teso Méndez, Félix
517
517.9
Fractional p-Laplacian
Bochner’s subordination
Semigroup formula
Extension problem
Balakrishnan’s formula
Spectral formulation
Análisis matemático
Ecuaciones diferenciales
1202 Análisis y Análisis Funcional
1202.07 Ecuaciones en Diferencias
title_short Three representations of the fractional p-Laplacian:semigroup, extension and Balakrishnan formulas
title_full Three representations of the fractional p-Laplacian:semigroup, extension and Balakrishnan formulas
title_fullStr Three representations of the fractional p-Laplacian:semigroup, extension and Balakrishnan formulas
title_full_unstemmed Three representations of the fractional p-Laplacian:semigroup, extension and Balakrishnan formulas
title_sort Three representations of the fractional p-Laplacian:semigroup, extension and Balakrishnan formulas
dc.creator.none.fl_str_mv Del Teso Méndez, Félix
Gómez-Castro, D.
Vázquez, Juan Luis
author Del Teso Méndez, Félix
author_facet Del Teso Méndez, Félix
Gómez-Castro, D.
Vázquez, Juan Luis
author_role author
author2 Gómez-Castro, D.
Vázquez, Juan Luis
author2_role author
author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 517
517.9
Fractional p-Laplacian
Bochner’s subordination
Semigroup formula
Extension problem
Balakrishnan’s formula
Spectral formulation
Análisis matemático
Ecuaciones diferenciales
1202 Análisis y Análisis Funcional
1202.07 Ecuaciones en Diferencias
topic 517
517.9
Fractional p-Laplacian
Bochner’s subordination
Semigroup formula
Extension problem
Balakrishnan’s formula
Spectral formulation
Análisis matemático
Ecuaciones diferenciales
1202 Análisis y Análisis Funcional
1202.07 Ecuaciones en Diferencias
description We introduce three representation formulas for the fractional p-Laplace operator in the whole range of parameters 0 < s < 1 and 1 < p < ∞. Note that for p ≠ 2 this a nonlinear operator. The first representation is based on a splitting procedure that combines a renormalized nonlinearity with the linear heat semigroup. The second adapts the nonlinearity to the Caffarelli-Silvestre linear extension technique. The third one is the corresponding nonlinear version of the Balakrishnan formula. We also discuss the correct choice of the constant of the fractional p-Laplace operator in order to have continuous dependence as p → 2 and s → 0+, 1−. A number of consequences and proposals are derived. Thus, we propose a natural spectral-type operator in domains, different from the standard restriction of the fractional p-Laplace operator acting on the whole space. We also propose numerical schemes, a new definition of the fractional p-Laplacian on manifolds, as well as alternative characterizations of the Ws, p(ℝn) seminorms.
publishDate 2021
dc.date.none.fl_str_mv 2021
2021-08-23
2021
2021-08-23
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/4992
url https://hdl.handle.net/20.500.14352/4992
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Spriger
publisher.none.fl_str_mv Spriger
dc.source.none.fl_str_mv reponame:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.300719

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