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

Abstract

Results on the convergence of minimizers and minimum values of integral and more general functionals Js: W1,p(Ωs) → ℝ on the sets Us(hs) = {v ∈ W1,p(Ωs): hs(v) ≤ 0 a.e. in Ωs}, where p > 1, {Ωs} is a sequence of domains contained in a bounded domain Ω of ℝn (n > 2), and {hs} is a sequence of functions on ℝ, are announced.