A limit case in non-isotropic two-phase minimization problems driven by p-Laplacians

In this work we study a minimization problem with two-phases where in each phase region the problem is ruled by a quasi-linear elliptic operator of p-Laplacian type. The problem in its variational form is as follows: min R ?\\fv0g 1 p jrvjp C p C C fCv dx C R ?\\fv60g 1 q jrvjq C q C fv dx : Here we...

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Detalles Bibliográficos
Publicado: 2018
Materias:
1 ∞ Laplacian
Free boundary problems
Non-isotropic two-phase problems
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14639963_v20_n3_p379_DaSilva
http://hdl.handle.net/20.500.12110/paper_14639963_v20_n3_p379_DaSilva
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_14639963_v20_n3_p379_DaSilva
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spelling paper:paper_14639963_v20_n3_p379_DaSilva2023-06-08T16:16:39Z A limit case in non-isotropic two-phase minimization problems driven by p-Laplacians 1 ∞ Laplacian Free boundary problems Non-isotropic two-phase problems In this work we study a minimization problem with two-phases where in each phase region the problem is ruled by a quasi-linear elliptic operator of p-Laplacian type. The problem in its variational form is as follows: min R ?\\fv0g 1 p jrvjp C p C C fCv dx C R ?\\fv60g 1 q jrvjq C q C fv dx : Here we minimize among all admissible functions v in an appropriate Sobolev space with a prescribed boundary datum v D g on @?. First, we show existence of a minimizer, prove some properties, and provide an example for non-uniqueness. Moreover, we analyze the limit case where p and q go to infinity, obtaining a limiting free boundary problem governed by the 1Laplacian operator. Consequently, Lipschitz regularity for any limiting solution is obtained. Finally, we establish some weak geometric properties for solutions. © European Mathematical Society 2018. 2018 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14639963_v20_n3_p379_DaSilva http://hdl.handle.net/20.500.12110/paper_14639963_v20_n3_p379_DaSilva
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic 1 ∞ Laplacian
Free boundary problems
Non-isotropic two-phase problems
spellingShingle 1 ∞ Laplacian
Free boundary problems
Non-isotropic two-phase problems
A limit case in non-isotropic two-phase minimization problems driven by p-Laplacians
topic_facet 1 ∞ Laplacian
Free boundary problems
Non-isotropic two-phase problems
description In this work we study a minimization problem with two-phases where in each phase region the problem is ruled by a quasi-linear elliptic operator of p-Laplacian type. The problem in its variational form is as follows: min R ?\\fv0g 1 p jrvjp C p C C fCv dx C R ?\\fv60g 1 q jrvjq C q C fv dx : Here we minimize among all admissible functions v in an appropriate Sobolev space with a prescribed boundary datum v D g on @?. First, we show existence of a minimizer, prove some properties, and provide an example for non-uniqueness. Moreover, we analyze the limit case where p and q go to infinity, obtaining a limiting free boundary problem governed by the 1Laplacian operator. Consequently, Lipschitz regularity for any limiting solution is obtained. Finally, we establish some weak geometric properties for solutions. © European Mathematical Society 2018.
title A limit case in non-isotropic two-phase minimization problems driven by p-Laplacians
title_short A limit case in non-isotropic two-phase minimization problems driven by p-Laplacians
title_full A limit case in non-isotropic two-phase minimization problems driven by p-Laplacians
title_fullStr A limit case in non-isotropic two-phase minimization problems driven by p-Laplacians
title_full_unstemmed A limit case in non-isotropic two-phase minimization problems driven by p-Laplacians
title_sort limit case in non-isotropic two-phase minimization problems driven by p-laplacians
publishDate 2018
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14639963_v20_n3_p379_DaSilva
http://hdl.handle.net/20.500.12110/paper_14639963_v20_n3_p379_DaSilva
_version_ 1768542098176344064

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