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ABSOLUTE CONTINUITY IN PERIODIC WAVEGUIDES

Published online by Cambridge University Press:  14 October 2002

ALEXANDER V. SOBOLEV  and
JONATHAN WALTHOE
ALEXANDER V. SOBOLEV
Affiliation:
Centre for Mathematical Analysis and its Applications, University of Sussex, Falmer, Brighton BN1 9QH. [email protected]
JONATHAN WALTHOE
Affiliation:
Centre for Mathematical Analysis and its Applications, University of Sussex, Falmer, Brighton BN1 9QH. [email protected]
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Abstract

We study second order elliptic operators with periodic coefficients in two-dimensional simply connected periodic waveguides with the Dirichlet or Neumann boundary conditions. It is proved that under some mild smoothness restrictions on the coefficients, such operators have purely absolutely continuous spectra. The proof follows a method suggested previously by A. Morame to tackle periodic operators with variable coefficients in dimension 2.

2000 Mathematical Subject Classification: 35J10, 35P05, 35J25.

Keywords

waveguidesabsolute continuityanalytic perturbations
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 85 , Issue 3 , November 2002 , pp. 717 - 741
Copyright
2002 London Mathematical Society

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