Finite element discretization of weighted $\hat{I}¦$-Laplace problems

Abstract

We study the finite element approximation of problems involving the weighted $\hat{I}¦$-Laplacian, where $\hat{I}¦$ is an $N$-function and the weight belongs to the class $A_{\hat{I}}¦$. 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.