A Singular Perturbation Problem for a Quasi-Linear Operator Satisfying the Natural Growth Condition of Lieberman
- Autores
- Martinez, Sandra Rita; Wolanski, Noemi Irene
- Año de publicación
- 2009
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- In this paper we study the following problem. For ε > 0, take uε as a solution of Luε := div ( g(|∇uε|) |∇uε| ∇uε) = βε(uε), uε ≥ 0. A solution to (Pε) is a function uε ∈ W1,G(Ω)∩L∞(Ω) such that Ω g(|∇uε|) ∇uε |∇uε| ∇ϕ dx = − Ω ϕ βε(uε) dx for every ϕ ∈ C∞0 (Ω). Here βε(s) = 1 ε β s ε , with β ∈ Lip(R), β > 0 in (0, 1) and β = 0 otherwise. We are interested in the limiting problem, when ε → 0. As in previous work with L = Δ or L = Δp we prove, under appropriate assumptions, that any limiting function is a weak solution to a free boundary problem. Moreover, for nondegenerate limits we prove that the reduced free boundary is a C1,α surface. This result is new even for Δp. Throughout the paper, we assume that g satisfies the conditions introduced by Lieberman in [Comm. Partial Differential Equations, 16 (1991), pp. 311-361].
Fil: Martinez, Sandra Rita. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Wolanski, Noemi Irene. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina - Materia
-
Free boundaries
Orlicz spaces
Singular perturbation - 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:11336/245145
Ver los metadatos del registro completo
id |
CONICETDig_ded1902abb3e2b19cb9eae8af5d003c3 |
---|---|
oai_identifier_str |
oai:ri.conicet.gov.ar:11336/245145 |
network_acronym_str |
CONICETDig |
repository_id_str |
3498 |
network_name_str |
CONICET Digital (CONICET) |
spelling |
A Singular Perturbation Problem for a Quasi-Linear Operator Satisfying the Natural Growth Condition of LiebermanMartinez, Sandra RitaWolanski, Noemi IreneFree boundariesOrlicz spacesSingular perturbationhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we study the following problem. For ε > 0, take uε as a solution of Luε := div ( g(|∇uε|) |∇uε| ∇uε) = βε(uε), uε ≥ 0. A solution to (Pε) is a function uε ∈ W1,G(Ω)∩L∞(Ω) such that Ω g(|∇uε|) ∇uε |∇uε| ∇ϕ dx = − Ω ϕ βε(uε) dx for every ϕ ∈ C∞0 (Ω). Here βε(s) = 1 ε β s ε , with β ∈ Lip(R), β > 0 in (0, 1) and β = 0 otherwise. We are interested in the limiting problem, when ε → 0. As in previous work with L = Δ or L = Δp we prove, under appropriate assumptions, that any limiting function is a weak solution to a free boundary problem. Moreover, for nondegenerate limits we prove that the reduced free boundary is a C1,α surface. This result is new even for Δp. Throughout the paper, we assume that g satisfies the conditions introduced by Lieberman in [Comm. Partial Differential Equations, 16 (1991), pp. 311-361].Fil: Martinez, Sandra Rita. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Wolanski, Noemi Irene. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaSociety for Industrial and Applied Mathematics2009-01info: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/11336/245145Martinez, Sandra Rita; Wolanski, Noemi Irene; A Singular Perturbation Problem for a Quasi-Linear Operator Satisfying the Natural Growth Condition of Lieberman; Society for Industrial and Applied Mathematics; Siam Journal On Mathematical Analysis; 41; 1; 1-2009; 318-3590036-1410CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://epubs.siam.org/doi/10.1137/070703740info:eu-repo/semantics/altIdentifier/doi/10.1137/070703740info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:11:33Zoai:ri.conicet.gov.ar:11336/245145instacron: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:34982025-09-29 10:11:33.459CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
A Singular Perturbation Problem for a Quasi-Linear Operator Satisfying the Natural Growth Condition of Lieberman |
title |
A Singular Perturbation Problem for a Quasi-Linear Operator Satisfying the Natural Growth Condition of Lieberman |
spellingShingle |
A Singular Perturbation Problem for a Quasi-Linear Operator Satisfying the Natural Growth Condition of Lieberman Martinez, Sandra Rita Free boundaries Orlicz spaces Singular perturbation |
title_short |
A Singular Perturbation Problem for a Quasi-Linear Operator Satisfying the Natural Growth Condition of Lieberman |
title_full |
A Singular Perturbation Problem for a Quasi-Linear Operator Satisfying the Natural Growth Condition of Lieberman |
title_fullStr |
A Singular Perturbation Problem for a Quasi-Linear Operator Satisfying the Natural Growth Condition of Lieberman |
title_full_unstemmed |
A Singular Perturbation Problem for a Quasi-Linear Operator Satisfying the Natural Growth Condition of Lieberman |
title_sort |
A Singular Perturbation Problem for a Quasi-Linear Operator Satisfying the Natural Growth Condition of Lieberman |
dc.creator.none.fl_str_mv |
Martinez, Sandra Rita Wolanski, Noemi Irene |
author |
Martinez, Sandra Rita |
author_facet |
Martinez, Sandra Rita Wolanski, Noemi Irene |
author_role |
author |
author2 |
Wolanski, Noemi Irene |
author2_role |
author |
dc.subject.none.fl_str_mv |
Free boundaries Orlicz spaces Singular perturbation |
topic |
Free boundaries Orlicz spaces Singular perturbation |
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 study the following problem. For ε > 0, take uε as a solution of Luε := div ( g(|∇uε|) |∇uε| ∇uε) = βε(uε), uε ≥ 0. A solution to (Pε) is a function uε ∈ W1,G(Ω)∩L∞(Ω) such that Ω g(|∇uε|) ∇uε |∇uε| ∇ϕ dx = − Ω ϕ βε(uε) dx for every ϕ ∈ C∞0 (Ω). Here βε(s) = 1 ε β s ε , with β ∈ Lip(R), β > 0 in (0, 1) and β = 0 otherwise. We are interested in the limiting problem, when ε → 0. As in previous work with L = Δ or L = Δp we prove, under appropriate assumptions, that any limiting function is a weak solution to a free boundary problem. Moreover, for nondegenerate limits we prove that the reduced free boundary is a C1,α surface. This result is new even for Δp. Throughout the paper, we assume that g satisfies the conditions introduced by Lieberman in [Comm. Partial Differential Equations, 16 (1991), pp. 311-361]. Fil: Martinez, Sandra Rita. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina Fil: Wolanski, Noemi Irene. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina |
description |
In this paper we study the following problem. For ε > 0, take uε as a solution of Luε := div ( g(|∇uε|) |∇uε| ∇uε) = βε(uε), uε ≥ 0. A solution to (Pε) is a function uε ∈ W1,G(Ω)∩L∞(Ω) such that Ω g(|∇uε|) ∇uε |∇uε| ∇ϕ dx = − Ω ϕ βε(uε) dx for every ϕ ∈ C∞0 (Ω). Here βε(s) = 1 ε β s ε , with β ∈ Lip(R), β > 0 in (0, 1) and β = 0 otherwise. We are interested in the limiting problem, when ε → 0. As in previous work with L = Δ or L = Δp we prove, under appropriate assumptions, that any limiting function is a weak solution to a free boundary problem. Moreover, for nondegenerate limits we prove that the reduced free boundary is a C1,α surface. This result is new even for Δp. Throughout the paper, we assume that g satisfies the conditions introduced by Lieberman in [Comm. Partial Differential Equations, 16 (1991), pp. 311-361]. |
publishDate |
2009 |
dc.date.none.fl_str_mv |
2009-01 |
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/11336/245145 Martinez, Sandra Rita; Wolanski, Noemi Irene; A Singular Perturbation Problem for a Quasi-Linear Operator Satisfying the Natural Growth Condition of Lieberman; Society for Industrial and Applied Mathematics; Siam Journal On Mathematical Analysis; 41; 1; 1-2009; 318-359 0036-1410 CONICET Digital CONICET |
url |
http://hdl.handle.net/11336/245145 |
identifier_str_mv |
Martinez, Sandra Rita; Wolanski, Noemi Irene; A Singular Perturbation Problem for a Quasi-Linear Operator Satisfying the Natural Growth Condition of Lieberman; Society for Industrial and Applied Mathematics; Siam Journal On Mathematical Analysis; 41; 1; 1-2009; 318-359 0036-1410 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://epubs.siam.org/doi/10.1137/070703740 info:eu-repo/semantics/altIdentifier/doi/10.1137/070703740 |
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 |
Society for Industrial and Applied Mathematics |
publisher.none.fl_str_mv |
Society for Industrial and Applied 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 |
_version_ |
1844614015741853696 |
score |
13.070432 |