Stable solutions of equations with a quadratic gradient term

Autores
Afonso Mourao Terra, Joana Isabel
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We consider positive solutions to a non-variational family of equations of the form−∆u − b(x)|∇u| 2 = λg(u) in Ω,where λ ≥ 0, b(x) is a given function, g is an increasing nonlinearity with g(0) > 0 and Ω ∈ R n isa bounded smooth domain. We introduce the definition of stability for nonvariational problemsand establish existence and regularity results for stable solutions. These results generalize theclasical results obtained when b(x) = b is a constant function making the problem variationalafter a suitable transformation.
Fil: Afonso Mourao Terra, Joana Isabel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; Argentina
Materia
Elliptic Equations
Gradient Quadratic term
stable 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:11336/18910
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Stable solutions of equations with a quadratic gradient termAfonso Mourao Terra, Joana IsabelElliptic EquationsGradient Quadratic termstable solutionshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We consider positive solutions to a non-variational family of equations of the form−∆u − b(x)|∇u| 2 = λg(u) in Ω,where λ ≥ 0, b(x) is a given function, g is an increasing nonlinearity with g(0) > 0 and Ω ∈ R n isa bounded smooth domain. We introduce the definition of stability for nonvariational problemsand establish existence and regularity results for stable solutions. These results generalize theclasical results obtained when b(x) = b is a constant function making the problem variationalafter a suitable transformation.Fil: Afonso Mourao Terra, Joana Isabel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; ArgentinaTexas State University. Department of Mathematics2016-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/18910Afonso Mourao Terra, Joana Isabel; Stable solutions of equations with a quadratic gradient term; Texas State University. Department of Mathematics; Electronic Journal of Differential Equations; 2016; 196; 9-2016; 1-221072-6691CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://ejde.math.txstate.edu/Volumes/2016/196/abstr.htmlinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:45:28Zoai:ri.conicet.gov.ar:11336/18910instacron: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 11:45:28.884CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Stable solutions of equations with a quadratic gradient term
title Stable solutions of equations with a quadratic gradient term
spellingShingle Stable solutions of equations with a quadratic gradient term
Afonso Mourao Terra, Joana Isabel
Elliptic Equations
Gradient Quadratic term
stable solutions
title_short Stable solutions of equations with a quadratic gradient term
title_full Stable solutions of equations with a quadratic gradient term
title_fullStr Stable solutions of equations with a quadratic gradient term
title_full_unstemmed Stable solutions of equations with a quadratic gradient term
title_sort Stable solutions of equations with a quadratic gradient term
dc.creator.none.fl_str_mv Afonso Mourao Terra, Joana Isabel
author Afonso Mourao Terra, Joana Isabel
author_facet Afonso Mourao Terra, Joana Isabel
author_role author
dc.subject.none.fl_str_mv Elliptic Equations
Gradient Quadratic term
stable solutions
topic Elliptic Equations
Gradient Quadratic term
stable 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 We consider positive solutions to a non-variational family of equations of the form−∆u − b(x)|∇u| 2 = λg(u) in Ω,where λ ≥ 0, b(x) is a given function, g is an increasing nonlinearity with g(0) > 0 and Ω ∈ R n isa bounded smooth domain. We introduce the definition of stability for nonvariational problemsand establish existence and regularity results for stable solutions. These results generalize theclasical results obtained when b(x) = b is a constant function making the problem variationalafter a suitable transformation.
Fil: Afonso Mourao Terra, Joana Isabel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; Argentina
description We consider positive solutions to a non-variational family of equations of the form−∆u − b(x)|∇u| 2 = λg(u) in Ω,where λ ≥ 0, b(x) is a given function, g is an increasing nonlinearity with g(0) > 0 and Ω ∈ R n isa bounded smooth domain. We introduce the definition of stability for nonvariational problemsand establish existence and regularity results for stable solutions. These results generalize theclasical results obtained when b(x) = b is a constant function making the problem variationalafter a suitable transformation.
publishDate 2016
dc.date.none.fl_str_mv 2016-09
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/11336/18910
Afonso Mourao Terra, Joana Isabel; Stable solutions of equations with a quadratic gradient term; Texas State University. Department of Mathematics; Electronic Journal of Differential Equations; 2016; 196; 9-2016; 1-22
1072-6691
CONICET Digital
CONICET
url http://hdl.handle.net/11336/18910
identifier_str_mv Afonso Mourao Terra, Joana Isabel; Stable solutions of equations with a quadratic gradient term; Texas State University. Department of Mathematics; Electronic Journal of Differential Equations; 2016; 196; 9-2016; 1-22
1072-6691
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://ejde.math.txstate.edu/Volumes/2016/196/abstr.html
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 Texas State University. Department of Mathematics
publisher.none.fl_str_mv Texas State University. Department of Mathematics
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 12.982451

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