# On the porosity of the free boundary in the $p(x)$-obstacle problem

### Samia Challal

York University, Toronto, Canada### Abdeslem Lyaghfouri

The Fields Institute for Research in Mathematical Sciences, Toronto, Canada

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## Abstract

In this paper we consider the obstacle problem for the $p(x)$-Laplace operator. Assuming that $p$ is locally Lipschitz continuous, we establish the growth rate of the solution near the free boundary from which we deduce its porosity.

## Cite this article

Samia Challal, Abdeslem Lyaghfouri, On the porosity of the free boundary in the $p(x)$-obstacle problem. Port. Math. 68 (2011), no. 1, pp. 109–123

DOI 10.4171/PM/1883