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JOURNALS // Nanosystems: Physics, Chemistry, Mathematics // Archive

Nanosystems: Physics, Chemistry, Mathematics, 2017 Volume 8, Issue 2, Pages 160–165 (Mi nano21)

MATHEMATICS

Waveguides with fast oscillating boundary

G. Cardone

University of Sannio, Department of Engineering, Corso Garibaldi, 107, 82100 Benevento, Italy

Abstract: We consider an elliptic operator in a planar waveguide with a fast oscillating boundary where we impose Dirichlet, Neumann or Robin boundary conditions assuming that both the period and the amplitude of the oscillations are small. We describe the homogenized operator, establish the norm resolvent convergence of the perturbed resolvent to the homogenized one, and prove the estimates for the rate of convergence. It is shown that under the homogenization, the type of the boundary condition can change.

Keywords: elliptic operator, unbounded domain, norm resolvent convergence.

Received: 04.01.2017
Revised: 29.01.2017

Language: English

DOI: 10.17586/2220-8054-2017-8-2-160-165



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