Norm-resolvent convergence for elliptic operators in domain with perforation along curve |
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| Authors: | Denis Borisov Giuseppe Cardone Tiziana Durante |
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| Institution: | 1. Institute of Mathematics CS USC RAS, Chernyshevsky str. 112, Ufa, 450008, Russian Federation;2. Bashkir State Pedagogical University, October St. 3a, Ufa, 450000, Russian Federation;3. University of Sannio, Department of Engineering, Corso Garibaldi, 107, 82100 Benevento, Italy;4. University of Salerno, Department of Information and Electrical Engineering and Applied Mathematics, Via Giovanni Paolo II, 132, 84084, Fisciano (SA), Italy |
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| 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. |
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