ABSOLUTE CONTINUITY IN PERIODIC WAVEGUIDES
Alexander V. Sobolev, JONATHAN WALTHOE · Proceedings of the London Mathematical Society · 2002
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.