Approximation of Solutions of the Neumann Problem in Disintegrating Domains
Vladimir Gilelevich Maz'ya, M. Hänler · Mathematische Nachrichten · 1993
Abstract This article deals with approximation of solutions of the Neumann problem in domains, where small tubes are cut out. With an increasing number of tubes some kind of a porous layer inside the domain is approximated. Our aim is to find an asymptotic solution for the separated limit domains. We show that this asymptotics is described by a boundary value problem for the two limit domains, where the solutions for each domain are connected by the boundary conditions.