On the convergence of solutions of variational problems with pointwise functional constraints in variable domains

We consider a sequence of convex integral functionals Fs : W1,p(Ωs) → ℝ and weakly lower semicontinuous and, in general, nonintegral Gs ℝ, where {Ωs} is domains ℝn contained bounded domain Ω ⊂ (n ⩾ 2) p > 1. Along with this, we closed sets Vs = {v ∈ Ms(v) ⩽ 0 a.e. Ωs}, Ms mapping from to the set all functions defined on Ωs. establish conditions under which minimizers minimum values +Gs converge minimizer value functional V W1,p(Ω) M(v) Ω}, M Ω.