Abstract. 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)) 0 a. e. in Ω s , where h : 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 . (2000): 49J45, 49J40, 35B27.
Mathematics subject classification
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.