Some New Results about Mosco Convergence

We consider the problem $\min\limits_{v\in\,C}J(v)$, where $J$ is the standard integral functional $$J(v) = \int_{\Omega} j(x,{\nabla v}) - \int_{\Omega} f(x)\,v(x),$$ defined in the Sobolev space $W_0^{1,q}(\Omega)$. We study the convergence of the minima $u$ if we perturb the convex set $C$ in accordance with the Mosco convergence.