Hopf's lemmas and boundary point results for the fractional p-Laplacian

Autores
Ochoa, Pablo; Salort, Ariel Martin
Año de publicación
2025
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper, we consider different versions of the classical Hopf’sboundary lemma in the setting of the fractional p−Laplacian for p ≥ 2. Westart by providing for a new proof to a Hopf’s lemma based on comparisonprinciples. Afterwards, we give a Hopf’s result for sign-changing potential describing the behavior of the fractional normal derivative of solutions aroundboundary points. The main contribution here is that we do not need to imposea global condition on the sign of the solution. Applications of the main resultsto boundary point lemmas and a discussion of non-local non-linear overdetermined problems are also provided.
Fil: Ochoa, Pablo. Universidad Nacional de Cuyo; Argentina
Fil: Salort, Ariel Martin. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Calculo. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Calculo; Argentina
Materia
HOPF LEMMA
FRACTIONAL P-LAPLACIAN
STRONG MINIMUM PRINCIPLE
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/290630
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/290630
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Hopf's lemmas and boundary point results for the fractional p-LaplacianOchoa, PabloSalort, Ariel MartinHOPF LEMMAFRACTIONAL P-LAPLACIANSTRONG MINIMUM PRINCIPLEhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper, we consider different versions of the classical Hopf’sboundary lemma in the setting of the fractional p−Laplacian for p ≥ 2. Westart by providing for a new proof to a Hopf’s lemma based on comparisonprinciples. Afterwards, we give a Hopf’s result for sign-changing potential describing the behavior of the fractional normal derivative of solutions aroundboundary points. The main contribution here is that we do not need to imposea global condition on the sign of the solution. Applications of the main resultsto boundary point lemmas and a discussion of non-local non-linear overdetermined problems are also provided.Fil: Ochoa, Pablo. Universidad Nacional de Cuyo; ArgentinaFil: Salort, Ariel Martin. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Calculo. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Calculo; ArgentinaAmerican Institute of Mathematical Sciences2025-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/290630Ochoa, Pablo; Salort, Ariel Martin; Hopf's lemmas and boundary point results for the fractional p-Laplacian; American Institute of Mathematical Sciences; Discrete And Continuous Dynamical Systems; 45; 3; 3-2025; 717-7341078-0947CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.aimsciences.org//article/doi/10.3934/dcds.2024109info:eu-repo/semantics/altIdentifier/doi/10.3934/dcds.2024109info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2026-08-25T15:07:49Zoai:ri.conicet.gov.ar:11336/290630instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982026-08-25 15:07:50.203CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Hopf's lemmas and boundary point results for the fractional p-Laplacian
title Hopf's lemmas and boundary point results for the fractional p-Laplacian
spellingShingle Hopf's lemmas and boundary point results for the fractional p-Laplacian
Ochoa, Pablo
HOPF LEMMA
FRACTIONAL P-LAPLACIAN
STRONG MINIMUM PRINCIPLE
title_short Hopf's lemmas and boundary point results for the fractional p-Laplacian
title_full Hopf's lemmas and boundary point results for the fractional p-Laplacian
title_fullStr Hopf's lemmas and boundary point results for the fractional p-Laplacian
title_full_unstemmed Hopf's lemmas and boundary point results for the fractional p-Laplacian
title_sort Hopf's lemmas and boundary point results for the fractional p-Laplacian
dc.creator.none.fl_str_mv Ochoa, Pablo
Salort, Ariel Martin
author Ochoa, Pablo
author_facet Ochoa, Pablo
Salort, Ariel Martin
author_role author
author2 Salort, Ariel Martin
author2_role author
dc.subject.none.fl_str_mv HOPF LEMMA
FRACTIONAL P-LAPLACIAN
STRONG MINIMUM PRINCIPLE
topic HOPF LEMMA
FRACTIONAL P-LAPLACIAN
STRONG MINIMUM PRINCIPLE
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this paper, we consider different versions of the classical Hopf’sboundary lemma in the setting of the fractional p−Laplacian for p ≥ 2. Westart by providing for a new proof to a Hopf’s lemma based on comparisonprinciples. Afterwards, we give a Hopf’s result for sign-changing potential describing the behavior of the fractional normal derivative of solutions aroundboundary points. The main contribution here is that we do not need to imposea global condition on the sign of the solution. Applications of the main resultsto boundary point lemmas and a discussion of non-local non-linear overdetermined problems are also provided.
Fil: Ochoa, Pablo. Universidad Nacional de Cuyo; Argentina
Fil: Salort, Ariel Martin. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Calculo. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Calculo; Argentina
description In this paper, we consider different versions of the classical Hopf’sboundary lemma in the setting of the fractional p−Laplacian for p ≥ 2. Westart by providing for a new proof to a Hopf’s lemma based on comparisonprinciples. Afterwards, we give a Hopf’s result for sign-changing potential describing the behavior of the fractional normal derivative of solutions aroundboundary points. The main contribution here is that we do not need to imposea global condition on the sign of the solution. Applications of the main resultsto boundary point lemmas and a discussion of non-local non-linear overdetermined problems are also provided.
publishDate 2025
dc.date.none.fl_str_mv 2025-03
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/290630
Ochoa, Pablo; Salort, Ariel Martin; Hopf's lemmas and boundary point results for the fractional p-Laplacian; American Institute of Mathematical Sciences; Discrete And Continuous Dynamical Systems; 45; 3; 3-2025; 717-734
1078-0947
CONICET Digital
CONICET
url http://hdl.handle.net/11336/290630
identifier_str_mv Ochoa, Pablo; Salort, Ariel Martin; Hopf's lemmas and boundary point results for the fractional p-Laplacian; American Institute of Mathematical Sciences; Discrete And Continuous Dynamical Systems; 45; 3; 3-2025; 717-734
1078-0947
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.aimsciences.org//article/doi/10.3934/dcds.2024109
info:eu-repo/semantics/altIdentifier/doi/10.3934/dcds.2024109
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Institute of Mathematical Sciences
publisher.none.fl_str_mv American Institute of Mathematical Sciences
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.265058

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