In this article we deal with a sequence of functionals defined on weighted Sobolev spaces. The spaces are associated with a sequence of domains Ω s contained in a bounded domain Ω of R n . The main structural components of the functionals are integral functionals whose integrands satisfy a growth and coercivity condition with a weight and additional terms ψ s ∈ L 1 ( Ω s ) . For the given functionals we consider variational problems with sets of constraints for functions v of the kind h(x,v(x)) 0a.e.in Ω s ,whereh : Ω × R → R . We establish conditions on h and ψ s and on the given domains, weighted spaces and functionals under which solutions of the variational problems under consideration converge in a certain sense to a solution of a limit variational problem with the set of constraints defined by the same function h .
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