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

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.

arXiv admin note: text overlap with arXiv:0912.2057 by other authors

References in corpus (1)

• Equivalence of Viscosity and Weak Solutions for the $p(x)$-Laplacian

Cited by in corpus (3)

• Regularity of Lipschitz free boundaries for a $p(x)$-Laplacian problem with right hand side
• Regularity in the two-phase Bernoulli problem for the $p$-Laplace operator
• Local and global $C^{1,\beta }$-regularity for uniformly elliptic quasilinear equations of $p$-Laplace and Orlicz-Laplace type