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

Published 1 Jun 2021 in math.AP | (2106.00439v1)

Abstract: 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.

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