We consider an infinite planar straight strip perforated by small holes along a curve. In such a 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.
|Titolo:||Homogenization and norm-resolvent convergence for elliptic operators in a strip perforated along a curve.|
|Data di pubblicazione:||2016|
|Appare nelle tipologie:||1.1.2 Articolo su rivista con ISSN|