Regularity of flat free boundaries for a \(p(x)\)-Laplacian problem with right hand side

We consider viscosity solutions to a one-phase free boundary problem for the \(p(x)\)-Laplacian with non-zero right hand side. We apply the tools developed in \cite{D} to prove that flat free boundaries are \(C^{1,\alpha}\). Moreover, we obtain some new results for the operator under consideration t...

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Bibliographic Details
Published in:arXiv.org 2021-06
Main Authors: Ferrari, Fausto, Lederman, Claudia
Format: Article
Language:English
Subjects:
Free boundaries
Online Access:Get full text
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Summary:We consider viscosity solutions to a one-phase free boundary problem for the \(p(x)\)-Laplacian with non-zero right hand side. We apply the tools developed in \cite{D} to prove that flat free boundaries are \(C^{1,\alpha}\). Moreover, we obtain some new results for the operator under consideration that are of independent interest.
ISSN:2331-8422