Finite element discretization of weighted $\mathrm{\Phi }$-Laplace problems

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