Stability of the Solutions of Nonlinear Weighted Elliptic Equations Without the Weighted Sobolev Spaces Framework

We prove some stability results on sequences of solutions of weighted elliptic equations such as $$-{\rm div}(s(x)|\nabla u_n |^{p-2}\,\nabla u_n) = f_n(x)\,,$$ under some assumptions on the convergence of the sequence $\{f_n\}$ (either weak or strong in some Lebesgue space). Here $s(x)$ is a positive weight belonging to the Sobolev space $W^{1,p}(\Omega)$.