Monotonicity of solutions for some nonlocal elliptic problems in half-spaces

Autores
Barrios, B.; del Pezzo, Leandro Martin; Garcia Melian, Jorge; Quaas, A.
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we consider classical solutions u of the semilinear fractional problem (- Δ) su= f(u) in R+N with u= 0 in RNR+N, where (- Δ) s, 0 < s< 1 , stands for the fractional laplacian, N≥ 2 , R+N={x=(x′,xN)∈RN:xN>0} is the half-space and f∈ C1 is a given function. With no additional restriction on the function f, we show that bounded, nonnegative, nontrivial classical solutions are indeed positive in R+N and verify (Formula presented.). This is in contrast with previously known results for the local case s= 1 , where nonnegative solutions which are not positive do exist and the monotonicity property above is not known to hold in general even for positive solutions when f(0) < 0.
Fil: Barrios, B.. Universidad de La Laguna; España
Fil: del Pezzo, Leandro Martin. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Garcia Melian, Jorge. Universidad de La Laguna; España
Fil: Quaas, A.. Universidad Técnica Federico Santa María; Chile
Materia
35S15
45M20
47G10
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:11336/60138
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Monotonicity of solutions for some nonlocal elliptic problems in half-spacesBarrios, B.del Pezzo, Leandro MartinGarcia Melian, JorgeQuaas, A.35S1545M2047G10https://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we consider classical solutions u of the semilinear fractional problem (- Δ) su= f(u) in R+N with u= 0 in RNR+N, where (- Δ) s, 0 < s< 1 , stands for the fractional laplacian, N≥ 2 , R+N={x=(x′,xN)∈RN:xN>0} is the half-space and f∈ C1 is a given function. With no additional restriction on the function f, we show that bounded, nonnegative, nontrivial classical solutions are indeed positive in R+N and verify (Formula presented.). This is in contrast with previously known results for the local case s= 1 , where nonnegative solutions which are not positive do exist and the monotonicity property above is not known to hold in general even for positive solutions when f(0) < 0.Fil: Barrios, B.. Universidad de La Laguna; EspañaFil: del Pezzo, Leandro Martin. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Garcia Melian, Jorge. Universidad de La Laguna; EspañaFil: Quaas, A.. Universidad Técnica Federico Santa María; ChileSpringer2017-04info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/60138Barrios, B.; del Pezzo, Leandro Martin; Garcia Melian, Jorge; Quaas, A.; Monotonicity of solutions for some nonlocal elliptic problems in half-spaces ; Springer; Calculus Of Variations And Partial Differential Equations; 56; 2; 4-2017; 1-160944-26691432-0835CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s00526-017-1133-9info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00526-017-1133-9info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1606.01061info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-26T08:40:04Zoai:ri.conicet.gov.ar:11336/60138instacron: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:34982025-11-26 08:40:05.193CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Monotonicity of solutions for some nonlocal elliptic problems in half-spaces
title Monotonicity of solutions for some nonlocal elliptic problems in half-spaces
spellingShingle Monotonicity of solutions for some nonlocal elliptic problems in half-spaces
Barrios, B.
35S15
45M20
47G10
title_short Monotonicity of solutions for some nonlocal elliptic problems in half-spaces
title_full Monotonicity of solutions for some nonlocal elliptic problems in half-spaces
title_fullStr Monotonicity of solutions for some nonlocal elliptic problems in half-spaces
title_full_unstemmed Monotonicity of solutions for some nonlocal elliptic problems in half-spaces
title_sort Monotonicity of solutions for some nonlocal elliptic problems in half-spaces
dc.creator.none.fl_str_mv Barrios, B.
del Pezzo, Leandro Martin
Garcia Melian, Jorge
Quaas, A.
author Barrios, B.
author_facet Barrios, B.
del Pezzo, Leandro Martin
Garcia Melian, Jorge
Quaas, A.
author_role author
author2 del Pezzo, Leandro Martin
Garcia Melian, Jorge
Quaas, A.
author2_role author
author
author
dc.subject.none.fl_str_mv 35S15
45M20
47G10
topic 35S15
45M20
47G10
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 classical solutions u of the semilinear fractional problem (- Δ) su= f(u) in R+N with u= 0 in RNR+N, where (- Δ) s, 0 < s< 1 , stands for the fractional laplacian, N≥ 2 , R+N={x=(x′,xN)∈RN:xN>0} is the half-space and f∈ C1 is a given function. With no additional restriction on the function f, we show that bounded, nonnegative, nontrivial classical solutions are indeed positive in R+N and verify (Formula presented.). This is in contrast with previously known results for the local case s= 1 , where nonnegative solutions which are not positive do exist and the monotonicity property above is not known to hold in general even for positive solutions when f(0) < 0.
Fil: Barrios, B.. Universidad de La Laguna; España
Fil: del Pezzo, Leandro Martin. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Garcia Melian, Jorge. Universidad de La Laguna; España
Fil: Quaas, A.. Universidad Técnica Federico Santa María; Chile
description In this paper we consider classical solutions u of the semilinear fractional problem (- Δ) su= f(u) in R+N with u= 0 in RNR+N, where (- Δ) s, 0 < s< 1 , stands for the fractional laplacian, N≥ 2 , R+N={x=(x′,xN)∈RN:xN>0} is the half-space and f∈ C1 is a given function. With no additional restriction on the function f, we show that bounded, nonnegative, nontrivial classical solutions are indeed positive in R+N and verify (Formula presented.). This is in contrast with previously known results for the local case s= 1 , where nonnegative solutions which are not positive do exist and the monotonicity property above is not known to hold in general even for positive solutions when f(0) < 0.
publishDate 2017
dc.date.none.fl_str_mv 2017-04
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/11336/60138
Barrios, B.; del Pezzo, Leandro Martin; Garcia Melian, Jorge; Quaas, A.; Monotonicity of solutions for some nonlocal elliptic problems in half-spaces ; Springer; Calculus Of Variations And Partial Differential Equations; 56; 2; 4-2017; 1-16
0944-2669
1432-0835
CONICET Digital
CONICET
url http://hdl.handle.net/11336/60138
identifier_str_mv Barrios, B.; del Pezzo, Leandro Martin; Garcia Melian, Jorge; Quaas, A.; Monotonicity of solutions for some nonlocal elliptic problems in half-spaces ; Springer; Calculus Of Variations And Partial Differential Equations; 56; 2; 4-2017; 1-16
0944-2669
1432-0835
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s00526-017-1133-9
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00526-017-1133-9
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1606.01061
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
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
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 13.011256

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