We consider an infinite strip perforated along a curve by small holes. In this perforated domain, we consider a scalar second-order elliptic differential operator subject to classical boundary conditions on the holes. Assuming that the perforation is non-periodic, we describe possible homogenized problems and prove the norm-resolvent convergence of the perturbed operator to a homogenized one. We also provide estimates for the rate of the convergence.
Norm-resolvent convergence for elliptic operators in domain with perforation along curve / Borisov, Denis; Cardone, G; Durante, Tiziana. - In: COMPTES RENDUS MATHÉMATIQUE. - ISSN 1631-073X. - 352:9(2014), pp. 679-683. [10.1016/j.crma.2014.07.003]
Norm-resolvent convergence for elliptic operators in domain with perforation along curve
Cardone G;
2014
Abstract
We consider an infinite strip perforated along a curve by small holes. In this perforated domain, we consider a scalar second-order elliptic differential operator subject to classical boundary conditions on the holes. Assuming that the perforation is non-periodic, we describe possible homogenized problems and prove the norm-resolvent convergence of the perturbed operator to a homogenized one. We also provide estimates for the rate of the convergence.File | Dimensione | Formato | |
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