Finite element discretization of weighted $\Phi$-Laplace problems

Abstract

We study the finite element approximation of problems involving the weighted $\Phi$-Laplacian, where $\Phi$ is an $N$-function and the weight belongs to the class $A_\Phi$. In particular, we consider a boundary value problem and an obstacle problem and derive error estimates in both cases. The analysis is based on the language of weighted Orlicz and weighted Orlicz--Sobolev spaces.