Homogenization and norm resolvent convergence for elliptic operators in a strip perforated along a curve

Abstract

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.

References in corpus (5)

• Interior error estimate for periodic homogenization
• Error estimate and unfolding for periodic homogenization
• Uniform resolvent convergence for strip with fast oscillating boundary
• Discrete spectrum of a pair of nonsymmetric waveguides coupled by a window
• Asymptotics for the solutions of elliptic systems with fast oscillating coefficients

Cited by in corpus (5)

• Norm-resolvent convergence of one-dimensional high-contrast periodic problems to a Kronig-Penney dipole-type model
• Embedded eigenvalues of the Neumann problem in a strip with a box-shaped perturbation
• The spectrum, radiation conditions and the Fredholm property for the Dirichlet Laplacian in a perforated plane with semi-infinite inclusions
• Gap opening in two-dimensional periodic systems
• A Strange Vertex Condition Coming From Nowhere