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
2019-01-01
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.File in questo prodotto:
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