The capacity method for asymptotic Dirichlet problems

Abstract

We prove that the asymptotic behaviour of the solutions of Dirichlet problems for second-order, linear, not necessarily symmetric elliptic equations in perforated domains of the form Ω_h=Ω\E_h is uniquely determined by the asymptotic behaviour, as h→∞, of suitable capacities of the sets B∩E_h, where B runs in a conveniently large class of subsets of Ω.