We study the homogenization of a general second order elliptic operator in an infinite planar straight strip perforated by small holes along a curve subject to classical boundary conditions on the holes under rather weak assumptions on the non-periodic perforation. We prove the norm resolvent convergence of the perturbed operator to a homogenized one in various operator norms, the estimates for the rate of convergence and the convergence of the spectrum.

Homogenization of elliptic operators in a strip perforated along a curve(Conference Paper)

Durante Tiziana
2019

Abstract

We study the homogenization of a general second order elliptic operator in an infinite planar straight strip perforated by small holes along a curve subject to classical boundary conditions on the holes under rather weak assumptions on the non-periodic perforation. We prove the norm resolvent convergence of the perturbed operator to a homogenized one in various operator norms, the estimates for the rate of convergence and the convergence of the spectrum.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11386/4729583
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