A Free boundary problem for the $p(x)$- Laplacian

Julián Fernández Bonder, Sandra Martínez, Noemi Wolanski

We consider the optimization problem of minimizing ${\int }_{\Omega }|\nabla u{|}^{p(x)}+\lambda {\chi }_{\{u>0\}}dx$ in the class of functions $W^{1,p(\cdot )}(\Omega )$ with $u-{\varphi }_0\in W_0^{1,p(\cdot )}(\Omega )$, for…