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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/60138
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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 Técnicas2025-10-22T11:07:26Zoai: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:34982025-10-22 11:07:26.471CONICET 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/ |
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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 |
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reponame:CONICET Digital (CONICET) instname:Consejo Nacional de Investigaciones Científicas y Técnicas |
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Consejo Nacional de Investigaciones Científicas y Técnicas |
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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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