Finite element approximation of the $p(\cdot )$-Laplacian

D. Breit, L. Diening, S. Schwarzacher

We study a~priori estimates for the Dirichlet problem of the $p(\cdot )$-Laplacian, \[-\mathrm{div}(|\nabla v|^{p(\cdot)-2} \nabla v) = f. \] We show that the gradients of the finit…