Existence of a BV solution for a mean curvature equation

Detalhes bibliográficos
Autor(a) principal: Pimenta, Marcos T.O. [UNESP]
Data de Publicação: 2021
Outros Autores: Montenegro, Marcelo
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1016/j.jde.2021.07.021
http://hdl.handle.net/11449/222061
Resumo: We prove the existence of a bounded variation solution for a quasilinear elliptic problem involving the mean curvature operator and a sublinear nonlinearity. We obtain such a solution as the limit of the solutions of another quasilinear elliptic problem involving a parameter p>1 as p→1+. The analysis requires estimates independent on p, as well as a precise version of the weak Euler-Lagrange equation satisfied by the solution.
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spelling Existence of a BV solution for a mean curvature equationExistence of solutionFunctions of bounded variationGeometric measure theoryMean curvature equationWe prove the existence of a bounded variation solution for a quasilinear elliptic problem involving the mean curvature operator and a sublinear nonlinearity. We obtain such a solution as the limit of the solutions of another quasilinear elliptic problem involving a parameter p>1 as p→1+. The analysis requires estimates independent on p, as well as a precise version of the weak Euler-Lagrange equation satisfied by the solution.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Universidade Estadual Paulista Unesp Departamento de Matemática e Computação, Rua Roberto Simonsen, 305Universidade Estadual de Campinas IMECC Departamento de Matemática, Rua Sérgio Buarque de Holanda, 651Universidade Estadual Paulista Unesp Departamento de Matemática e Computação, Rua Roberto Simonsen, 305FAPESP: 2019/02512-5FAPESP: 2019/14330-9CNPq: 303788/2018-6Universidade Estadual Paulista (UNESP)Universidade Estadual de Campinas (UNICAMP)Pimenta, Marcos T.O. [UNESP]Montenegro, Marcelo2022-04-28T19:42:09Z2022-04-28T19:42:09Z2021-10-25info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article51-64http://dx.doi.org/10.1016/j.jde.2021.07.021Journal of Differential Equations, v. 299, p. 51-64.1090-27320022-0396http://hdl.handle.net/11449/22206110.1016/j.jde.2021.07.0212-s2.0-85111297667Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengJournal of Differential Equationsinfo:eu-repo/semantics/openAccess2022-04-28T19:42:09Zoai:repositorio.unesp.br:11449/222061Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T16:59:19.830009Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Existence of a BV solution for a mean curvature equation
title Existence of a BV solution for a mean curvature equation
spellingShingle Existence of a BV solution for a mean curvature equation
Pimenta, Marcos T.O. [UNESP]
Existence of solution
Functions of bounded variation
Geometric measure theory
Mean curvature equation
title_short Existence of a BV solution for a mean curvature equation
title_full Existence of a BV solution for a mean curvature equation
title_fullStr Existence of a BV solution for a mean curvature equation
title_full_unstemmed Existence of a BV solution for a mean curvature equation
title_sort Existence of a BV solution for a mean curvature equation
author Pimenta, Marcos T.O. [UNESP]
author_facet Pimenta, Marcos T.O. [UNESP]
Montenegro, Marcelo
author_role author
author2 Montenegro, Marcelo
author2_role author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (UNESP)
Universidade Estadual de Campinas (UNICAMP)
dc.contributor.author.fl_str_mv Pimenta, Marcos T.O. [UNESP]
Montenegro, Marcelo
dc.subject.por.fl_str_mv Existence of solution
Functions of bounded variation
Geometric measure theory
Mean curvature equation
topic Existence of solution
Functions of bounded variation
Geometric measure theory
Mean curvature equation
description We prove the existence of a bounded variation solution for a quasilinear elliptic problem involving the mean curvature operator and a sublinear nonlinearity. We obtain such a solution as the limit of the solutions of another quasilinear elliptic problem involving a parameter p>1 as p→1+. The analysis requires estimates independent on p, as well as a precise version of the weak Euler-Lagrange equation satisfied by the solution.
publishDate 2021
dc.date.none.fl_str_mv 2021-10-25
2022-04-28T19:42:09Z
2022-04-28T19:42:09Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://dx.doi.org/10.1016/j.jde.2021.07.021
Journal of Differential Equations, v. 299, p. 51-64.
1090-2732
0022-0396
http://hdl.handle.net/11449/222061
10.1016/j.jde.2021.07.021
2-s2.0-85111297667
url http://dx.doi.org/10.1016/j.jde.2021.07.021
http://hdl.handle.net/11449/222061
identifier_str_mv Journal of Differential Equations, v. 299, p. 51-64.
1090-2732
0022-0396
10.1016/j.jde.2021.07.021
2-s2.0-85111297667
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Journal of Differential Equations
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 51-64
dc.source.none.fl_str_mv Scopus
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv
_version_ 1808128731616641024

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