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

Abstract

In this paper, we give sufficient conditions for the convergence of minimizers and minimum values of integral and more general functionals0 a.e. in Ω s }, where p > 1, {Ω s } is a sequence of domains contained in a bounded domain Ω of R n (n 2), and {h s } is a sequence of functions on R. In so doing, we assume that the considered functionals Γ -converge to a functional defined on W 1, p (Ω) and the spaces W 1, p (Ω s ) are strongly connected with the space W 1, p (Ω). Certain conditions on the relation between the functions h s and a function h : R → R are also required in our main results.