On the Convergence of Solutions of Variational Problems with Implicit Pointwise Constraints in Variable Domains

Results on the convergence of minimizers and minimum values of integral and more general functionals $J_s\colon W^{1,p}(\Omega_s)\to\mathbb R$ on the sets $U_s(h_s)=\{v\in W^{1,p}(\Omega_s)\colon h_s(v)\leqslant 0\ \text{a.e.\ in }\Omega_s\}$, where $p>1$, $\{\Omega_s\}$ is a sequence of domains contained in a bounded domain $\Omega$ of $\mathbb R^n$ ($n\geqslant 2$), and $\{h_s\}$ is a sequence of functions on $\mathbb R$, are announced.