Homogenization of elliptic operators in a strip perforated along a curve

摘要

We study the homogenization of a general second order elliptic operator in an infinite planar straight strip perforated by small holes along a curve subject to classical boundary conditions on the holes under rather weak assumptions on the non-periodic perforation. We prove the norm resolvent convergence of the perturbed operator to a homogenized one in various operator norms, the estimates for the rate of convergence and the convergence of the spectrum.