The capacity method for asymptotic Dirichlet problems

Abstract

We prove that the asymptotic behaviour of the solutions of Dirichlet problems for linear elliptic equations in perforated domains of the form Ωh = Ω Eh is uniquely determined by the asymptotic behaviour, as h →∞ , of suitable capacities of the sets B∩Eh , where B runs in a conveniently large class of subsets of Ω. Authors’ address: Gianni Dal Maso, SISSA, via Beirut 4, 34013 Trieste (Italy) Adriana Garroni, SISSA, via Beirut 4, 34013 Trieste (Italy) Abbreviated title: Capacity method for asymptotic Dirichlet problems The capacity method for asymptotic Dirichlet problems