1. Norm-resolvent convergence for elliptic operators in domain with perforation along curve
- Author
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Tiziana Durante, Denis Borisov, Giuseppe Cardone, Borisov, Deni, Cardone, G, and Durante, Tiziana
- Subjects
Elliptic curve point multiplication ,Elliptic operator ,norm resolvent convergence ,Physics::Instrumentation and Detectors ,Norm (mathematics) ,Elliptic operators ,Mathematical analysis ,Elliptic operators, norm resolvent convergence ,General Medicine ,Boundary value problem ,Differential operator ,Resolvent ,Mathematics - 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.
- Published
- 2014
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