%0 Journal Article
%T Homogenization and norm resolvent convergence for elliptic operators in a strip perforated along a curve
%A Denis Borisov
%A Giuseppe Cardone
%A Tiziana Durante
%J Mathematics
%D 2013
%I arXiv
%X We consider an infinite planar straight strip perforated by small holes along a curve. In such domain, we consider a general second order elliptic operator subject to classical boundary conditions on the holes. Assuming that the perforation is non-periodic and satisfies rather weak assumptions, we describe all possible homogenized problems. Our main result is the norm resolvent convergence of the perturbed operator to a homogenized one in various operator norms and the estimates for the rate of convergence. On the basis of the norm resolvent convergence, we prove the convergence of the spectrum.
%U http://arxiv.org/abs/1305.1009v3