Weak solutions and regularity of the interface in an inhomogeneous free boundary problem for the p (x)-Laplacian

In this paper we study a one phase free boundary problem for the p (x)-Laplacian with non-zero right hand side. We prove that the free boundary of a weak solution is a C1,α surface in a neighborhood of every "flat" free boundary point. We also obtain further regularity results on the free...

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Autores principales: Lederman, Claudia Beatriz, Wolanski, Noemi Irene
Publicado: 2017
Materias:
Free boundary problem
Inhomogeneous problem
Regularity of the free boundary
Singular perturbation
Variable exponent spaces
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14639963_v19_n2_p201_Lederman
http://hdl.handle.net/20.500.12110/paper_14639963_v19_n2_p201_Lederman
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_14639963_v19_n2_p201_Lederman
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spelling paper:paper_14639963_v19_n2_p201_Lederman2023-06-08T16:16:38Z Weak solutions and regularity of the interface in an inhomogeneous free boundary problem for the p (x)-Laplacian Lederman, Claudia Beatriz Wolanski, Noemi Irene Free boundary problem Inhomogeneous problem Regularity of the free boundary Singular perturbation Variable exponent spaces In this paper we study a one phase free boundary problem for the p (x)-Laplacian with non-zero right hand side. We prove that the free boundary of a weak solution is a C1,α surface in a neighborhood of every "flat" free boundary point. We also obtain further regularity results on the free boundary, under further regularity assumptions on the data. We apply these results to limit functions of an inhomogeneous singular perturbation problem for the p (x)-Laplacian that we studied in [25]. © European Mathematical Society 2017. Fil:Lederman, C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Wolanski, N. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2017 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14639963_v19_n2_p201_Lederman http://hdl.handle.net/20.500.12110/paper_14639963_v19_n2_p201_Lederman
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Free boundary problem
Inhomogeneous problem
Regularity of the free boundary
Singular perturbation
Variable exponent spaces
spellingShingle Free boundary problem
Inhomogeneous problem
Regularity of the free boundary
Singular perturbation
Variable exponent spaces
Lederman, Claudia Beatriz
Wolanski, Noemi Irene
Weak solutions and regularity of the interface in an inhomogeneous free boundary problem for the p (x)-Laplacian
topic_facet Free boundary problem
Inhomogeneous problem
Regularity of the free boundary
Singular perturbation
Variable exponent spaces
description In this paper we study a one phase free boundary problem for the p (x)-Laplacian with non-zero right hand side. We prove that the free boundary of a weak solution is a C1,α surface in a neighborhood of every "flat" free boundary point. We also obtain further regularity results on the free boundary, under further regularity assumptions on the data. We apply these results to limit functions of an inhomogeneous singular perturbation problem for the p (x)-Laplacian that we studied in [25]. © European Mathematical Society 2017.
author Lederman, Claudia Beatriz
Wolanski, Noemi Irene
author_facet Lederman, Claudia Beatriz
Wolanski, Noemi Irene
author_sort Lederman, Claudia Beatriz
title Weak solutions and regularity of the interface in an inhomogeneous free boundary problem for the p (x)-Laplacian
title_short Weak solutions and regularity of the interface in an inhomogeneous free boundary problem for the p (x)-Laplacian
title_full Weak solutions and regularity of the interface in an inhomogeneous free boundary problem for the p (x)-Laplacian
title_fullStr Weak solutions and regularity of the interface in an inhomogeneous free boundary problem for the p (x)-Laplacian
title_full_unstemmed Weak solutions and regularity of the interface in an inhomogeneous free boundary problem for the p (x)-Laplacian
title_sort weak solutions and regularity of the interface in an inhomogeneous free boundary problem for the p (x)-laplacian
publishDate 2017
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14639963_v19_n2_p201_Lederman
http://hdl.handle.net/20.500.12110/paper_14639963_v19_n2_p201_Lederman
work_keys_str_mv AT ledermanclaudiabeatriz weaksolutionsandregularityoftheinterfaceinaninhomogeneousfreeboundaryproblemforthepxlaplacian
AT wolanskinoemiirene weaksolutionsandregularityoftheinterfaceinaninhomogeneousfreeboundaryproblemforthepxlaplacian
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