Journal
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
Volume 64, Issue 3, Pages 439-472Publisher
SPRINGER INTERNATIONAL PUBLISHING AG
DOI: 10.1007/s00033-012-0264-2
Keywords
Waveguide; Alternating boundary conditions; Uniform resolvent convergence; Band spectrum; Asymptotics
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Funding
- RFBR
- Federal Task Program Scientific and Pedagogical Staff of Innovative Russia [02.640.11.0612]
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We consider a magnetic Schrodinger operator in a planar infinite strip with frequently and non-periodically alternating Dirichlet and Robin boundary conditions. Assuming that the homogenized boundary condition is the Dirichlet or the Robin one, we establish the uniform resolvent convergence in various operator norms and we prove the estimates for the rates of convergence. It is shown that these estimates can be improved by using special boundary correctors. In the case of periodic alternation, pure Laplacian, and the homogenized Robin boundary condition, we construct two-terms asymptotics for the first band functions, as well as the complete asymptotics expansion (up to an exponentially small term) for the bottom of the band spectrum.
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