Continuity of some non-local functionals with respect to a convergence of the underlying measures

Abstract

We study some non-local functionals on the Sobolev space W01,p(Ω) involving a double integral on Ω×Ω with respect to a measure μ. We introduce a suitable notion of convergence of measures on product spaces which implies a stability property in the sense of the Γ-convergence of the corresponding functionals.