Variational problems with pointwise constraints and degeneration in variable domains
Alexander Albertovich Kovalevsky, Olga A. Rudakova · Differential Equations & Applications · 2009
In this article we deal with a sequence of functionals defined on weighted Sobolev spaces. The spaces are associated with a sequence of domains s contained in a bounded domain 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 s L 1 ( 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 s , where h : R R . We establish conditions on h and 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 .