Effective permeability of the boundary of a domain

Abstract

Abstract Let u be a solution of the Laplace equation in a boilnded domain Ω in R n whose boundary consists of two disjoint surfaces λ0 and λ1. On λ1 u satisfies a Dirichlet boundary condition, whereas on Λ0 u satisfies the impermeability condition ∂u/∂n = 0 ever3 where except on m, small “holes” λ, separated from one another by distance of older of magnitude ε. and u= O on the holes. In this paper wr study the effective periwabilitv of the surface λ0as ε→0.