Symmetry results in the half-space for a semi-linear fractional Laplace equation

Autores
Barrios, B.; del Pezzo, Leandro Martin; Garcia Melian, Jorge; Quaas, A.
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper, we analyze the semi-linear fractional Laplace equation (−)s u = f (u) in RN +, u = 0 in RN \RN +, where RN + = {x = (x , xN ) ∈ RN : xN > 0} stands for the half-space and f is a locally Lipschitz nonlinearity. We completely characterize one-dimensional bounded solutions of this problem, and we prove among other things that if u is a bounded solution with ρ := supRN u verifying f (ρ) = 0, then u is necessarily one dimensional.
Fil: Barrios, B.. Universidad de La Laguna; España
Fil: del Pezzo, Leandro Martin. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Torcuato Di Tella. Instituto "Torcuato Di Tella"; Argentina
Fil: Garcia Melian, Jorge. Universidad de La Laguna; España
Fil: Quaas, A.. Universidad Técnica Federico Santa María. Departamento de Matemática; Chile
Materia
ENERGY FORMULAS
FRACTIONAL LAPLACIAN
ONE-DIMENSIONAL ANAYSIS
SYMMETRY SOLUTIONS
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:11336/98186
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/98186
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Symmetry results in the half-space for a semi-linear fractional Laplace equationBarrios, B.del Pezzo, Leandro MartinGarcia Melian, JorgeQuaas, A.ENERGY FORMULASFRACTIONAL LAPLACIANONE-DIMENSIONAL ANAYSISSYMMETRY SOLUTIONShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper, we analyze the semi-linear fractional Laplace equation (−)s u = f (u) in RN +, u = 0 in RN \RN +, where RN + = {x = (x , xN ) ∈ RN : xN > 0} stands for the half-space and f is a locally Lipschitz nonlinearity. We completely characterize one-dimensional bounded solutions of this problem, and we prove among other things that if u is a bounded solution with ρ := supRN u verifying f (ρ) = 0, then u is necessarily one dimensional.Fil: Barrios, B.. Universidad de La Laguna; EspañaFil: del Pezzo, Leandro Martin. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Torcuato Di Tella. Instituto "Torcuato Di Tella"; ArgentinaFil: Garcia Melian, Jorge. Universidad de La Laguna; EspañaFil: Quaas, A.. Universidad Técnica Federico Santa María. Departamento de Matemática; ChileSpringer Heidelberg2018-03info: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/11336/98186Barrios, B.; del Pezzo, Leandro Martin; Garcia Melian, Jorge; Quaas, A.; Symmetry results in the half-space for a semi-linear fractional Laplace equation; Springer Heidelberg; Annali Di Matematica Pura Ed Applicata; 197; 5; 3-2018; 1385-14160373-3114CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007%2Fs10231-018-0729-9info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs10231-018-0729-9info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:10:26Zoai:ri.conicet.gov.ar:11336/98186instacron: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:34982025-09-03 10:10:27.156CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Symmetry results in the half-space for a semi-linear fractional Laplace equation
title Symmetry results in the half-space for a semi-linear fractional Laplace equation
spellingShingle Symmetry results in the half-space for a semi-linear fractional Laplace equation
Barrios, B.
ENERGY FORMULAS
FRACTIONAL LAPLACIAN
ONE-DIMENSIONAL ANAYSIS
SYMMETRY SOLUTIONS
title_short Symmetry results in the half-space for a semi-linear fractional Laplace equation
title_full Symmetry results in the half-space for a semi-linear fractional Laplace equation
title_fullStr Symmetry results in the half-space for a semi-linear fractional Laplace equation
title_full_unstemmed Symmetry results in the half-space for a semi-linear fractional Laplace equation
title_sort Symmetry results in the half-space for a semi-linear fractional Laplace equation
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 ENERGY FORMULAS
FRACTIONAL LAPLACIAN
ONE-DIMENSIONAL ANAYSIS
SYMMETRY SOLUTIONS
topic ENERGY FORMULAS
FRACTIONAL LAPLACIAN
ONE-DIMENSIONAL ANAYSIS
SYMMETRY SOLUTIONS
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 analyze the semi-linear fractional Laplace equation (−)s u = f (u) in RN +, u = 0 in RN \RN +, where RN + = {x = (x , xN ) ∈ RN : xN > 0} stands for the half-space and f is a locally Lipschitz nonlinearity. We completely characterize one-dimensional bounded solutions of this problem, and we prove among other things that if u is a bounded solution with ρ := supRN u verifying f (ρ) = 0, then u is necessarily one dimensional.
Fil: Barrios, B.. Universidad de La Laguna; España
Fil: del Pezzo, Leandro Martin. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Torcuato Di Tella. Instituto "Torcuato Di Tella"; Argentina
Fil: Garcia Melian, Jorge. Universidad de La Laguna; España
Fil: Quaas, A.. Universidad Técnica Federico Santa María. Departamento de Matemática; Chile
description In this paper, we analyze the semi-linear fractional Laplace equation (−)s u = f (u) in RN +, u = 0 in RN \RN +, where RN + = {x = (x , xN ) ∈ RN : xN > 0} stands for the half-space and f is a locally Lipschitz nonlinearity. We completely characterize one-dimensional bounded solutions of this problem, and we prove among other things that if u is a bounded solution with ρ := supRN u verifying f (ρ) = 0, then u is necessarily one dimensional.
publishDate 2018
dc.date.none.fl_str_mv 2018-03
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/11336/98186
Barrios, B.; del Pezzo, Leandro Martin; Garcia Melian, Jorge; Quaas, A.; Symmetry results in the half-space for a semi-linear fractional Laplace equation; Springer Heidelberg; Annali Di Matematica Pura Ed Applicata; 197; 5; 3-2018; 1385-1416
0373-3114
CONICET Digital
CONICET
url http://hdl.handle.net/11336/98186
identifier_str_mv Barrios, B.; del Pezzo, Leandro Martin; Garcia Melian, Jorge; Quaas, A.; Symmetry results in the half-space for a semi-linear fractional Laplace equation; Springer Heidelberg; Annali Di Matematica Pura Ed Applicata; 197; 5; 3-2018; 1385-1416
0373-3114
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%2Fs10231-018-0729-9
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs10231-018-0729-9
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 Heidelberg
publisher.none.fl_str_mv Springer Heidelberg
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 13.13397

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