We study the finite element approximation of problems involving the weighted $p$-Laplacian for $p \in (1,\infty)$ and weights belonging to the Muckenhoupt class $A_1$. In particular, we consider an equation and an obstacle problem for the weighted $p$-Laplacian and derive error estimates in both cases. The analysis is based on the language of weighted Orlicz and Orlicz--Sobolev spaces.

翻译：我们研究了涉及加权$p$-Laplacian问题的有限元逼近方法，其中$p \in (1,\infty)$且权函数属于Muckenhoupt类$A_1$。具体而言，我们分别针对加权$p$-Laplacian方程及其障碍问题展开讨论，并推导了两种情形下的误差估计。该分析基于加权Orlicz空间与Orlicz--Sobolev空间的数学语言框架。