The two membranes problem for fully nonlinear operators

Autores
Caffarelli, Luis; Duque, Luis; Vivas, Hernán Agustín
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study the two membranes problem for two different fully nonlinear operators. We give a viscosity formulation for the problem and prove existence of solutions. Then we prove a general regularity result and the optimal C1,1 regularity when the operators are the Pucci extremal operators. We also give an example that shows that no regularity for the free boundary is to be expected to hold in general.
Fil: Caffarelli, Luis. University of Texas at Austin; Estados Unidos
Fil: Duque, Luis. University of Texas at Austin; Estados Unidos
Fil: Vivas, Hernán Agustín. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata; Argentina
Materia
FREE BOUNDARY PROBLEMS
FULLY NONLINEAR
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:11336/100972
Acceder
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network_name_str CONICET Digital (CONICET)
spelling The two membranes problem for fully nonlinear operatorsCaffarelli, LuisDuque, LuisVivas, Hernán AgustínFREE BOUNDARY PROBLEMSFULLY NONLINEARhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study the two membranes problem for two different fully nonlinear operators. We give a viscosity formulation for the problem and prove existence of solutions. Then we prove a general regularity result and the optimal C1,1 regularity when the operators are the Pucci extremal operators. We also give an example that shows that no regularity for the free boundary is to be expected to hold in general.Fil: Caffarelli, Luis. University of Texas at Austin; Estados UnidosFil: Duque, Luis. University of Texas at Austin; Estados UnidosFil: Vivas, Hernán Agustín. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata; ArgentinaAmerican Institute of Mathematical Sciences2018-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/zipapplication/pdfhttp://hdl.handle.net/11336/100972Caffarelli, Luis; Duque, Luis; Vivas, Hernán Agustín; The two membranes problem for fully nonlinear operators; American Institute of Mathematical Sciences; Discrete And Continuous Dynamical Systems; 38; 12; 12-2018; 6015-60271078-0947CONICET DigitalCONICETenghttp://hdl.handle.net/11336/92009info:eu-repo/semantics/altIdentifier/url/http://www.aimsciences.org/article/doi/10.3934/dcds.2018152info:eu-repo/semantics/altIdentifier/doi/10.3934/dcds.2018152info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1708.09420info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:36:00Zoai:ri.conicet.gov.ar:11336/100972instacron: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 09:36:00.572CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The two membranes problem for fully nonlinear operators
title The two membranes problem for fully nonlinear operators
spellingShingle The two membranes problem for fully nonlinear operators
Caffarelli, Luis
FREE BOUNDARY PROBLEMS
FULLY NONLINEAR
title_short The two membranes problem for fully nonlinear operators
title_full The two membranes problem for fully nonlinear operators
title_fullStr The two membranes problem for fully nonlinear operators
title_full_unstemmed The two membranes problem for fully nonlinear operators
title_sort The two membranes problem for fully nonlinear operators
dc.creator.none.fl_str_mv Caffarelli, Luis
Duque, Luis
Vivas, Hernán Agustín
author Caffarelli, Luis
author_facet Caffarelli, Luis
Duque, Luis
Vivas, Hernán Agustín
author_role author
author2 Duque, Luis
Vivas, Hernán Agustín
author2_role author
author
dc.subject.none.fl_str_mv FREE BOUNDARY PROBLEMS
FULLY NONLINEAR
topic FREE BOUNDARY PROBLEMS
FULLY NONLINEAR
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 study the two membranes problem for two different fully nonlinear operators. We give a viscosity formulation for the problem and prove existence of solutions. Then we prove a general regularity result and the optimal C1,1 regularity when the operators are the Pucci extremal operators. We also give an example that shows that no regularity for the free boundary is to be expected to hold in general.
Fil: Caffarelli, Luis. University of Texas at Austin; Estados Unidos
Fil: Duque, Luis. University of Texas at Austin; Estados Unidos
Fil: Vivas, Hernán Agustín. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata; Argentina
description We study the two membranes problem for two different fully nonlinear operators. We give a viscosity formulation for the problem and prove existence of solutions. Then we prove a general regularity result and the optimal C1,1 regularity when the operators are the Pucci extremal operators. We also give an example that shows that no regularity for the free boundary is to be expected to hold in general.
publishDate 2018
dc.date.none.fl_str_mv 2018-12
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/11336/100972
Caffarelli, Luis; Duque, Luis; Vivas, Hernán Agustín; The two membranes problem for fully nonlinear operators; American Institute of Mathematical Sciences; Discrete And Continuous Dynamical Systems; 38; 12; 12-2018; 6015-6027
1078-0947
CONICET Digital
CONICET
url http://hdl.handle.net/11336/100972
identifier_str_mv Caffarelli, Luis; Duque, Luis; Vivas, Hernán Agustín; The two membranes problem for fully nonlinear operators; American Institute of Mathematical Sciences; Discrete And Continuous Dynamical Systems; 38; 12; 12-2018; 6015-6027
1078-0947
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv http://hdl.handle.net/11336/92009
info:eu-repo/semantics/altIdentifier/url/http://www.aimsciences.org/article/doi/10.3934/dcds.2018152
info:eu-repo/semantics/altIdentifier/doi/10.3934/dcds.2018152
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1708.09420
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/zip
application/pdf
dc.publisher.none.fl_str_mv American Institute of Mathematical Sciences
publisher.none.fl_str_mv American Institute of Mathematical Sciences
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 13.070432

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