The Dirichlet problem for the $p(x)$-Laplacian with unbounded exponent $p(x)$

M. Khamsi, J. Lang, O. Mendez +1

We prove the solvability of the Dirichlet problem for the variable exponent $p$-Laplacian with boundary data in $W^{1,p(x)}(\Omega )$ on a bounded, smooth domain $\Omega \subset {\mathbb{R}}^n$…