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, C., Wolanski, N.
Formato: JOUR
Materias:
Free boundary problem
Inhomogeneous problem
Regularity of the free boundary
Singular perturbation
Variable exponent spaces
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_14639963_v19_n2_p201_Lederman
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_14639963_v19_n2_p201_Lederman2023-10-03T16:17:04Z Weak solutions and regularity of the interface in an inhomogeneous free boundary problem for the p (x)-Laplacian Lederman, C. Wolanski, N. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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, C.
Wolanski, N.
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.
format JOUR
author Lederman, C.
Wolanski, N.
author_facet Lederman, C.
Wolanski, N.
author_sort Lederman, C.
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
url http://hdl.handle.net/20.500.12110/paper_14639963_v19_n2_p201_Lederman
work_keys_str_mv AT ledermanc weaksolutionsandregularityoftheinterfaceinaninhomogeneousfreeboundaryproblemforthepxlaplacian
AT wolanskin weaksolutionsandregularityoftheinterfaceinaninhomogeneousfreeboundaryproblemforthepxlaplacian
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