Absolute continuity in periodic waveguides. (English) Zbl 1247.35077
Summary: 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.
MSC:
35P05 | General topics in linear spectral theory for PDEs |
35B10 | Periodic solutions to PDEs |
35J10 | Schrödinger operator, Schrödinger equation |