Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 42, Issue 36, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1751-8113/42/36/365205
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Funding
- RFBR [09-01-00530]
- President of Russian Federation for young scientists [NSh-2215.2008.1]
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We consider the Laplacian in a planar strip with a Dirichlet boundary condition on the upper boundary and with a frequent alternation boundary condition on the lower boundary. The alternation is introduced by the periodic partition of the boundary into small segments on which Dirichlet and Neumann conditions are imposed in turns. We show that under certain conditions the homogenized operator is the Dirichlet Laplacian and prove the uniform resolvent convergence. The spectrum of the perturbed operator consists of its essential part only and has a band structure. We construct the leading terms of the asymptotic expansions for the first band functions. We also construct the complete asymptotic expansion for the bottom of the spectrum.
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