3 Sep 2008; Mat-Nat Faculty (UiTø), room A228. Wednesday 10:15-12:00
Sergey Nazarov (Institute of Mechanical Engineering Problems, St. Petersburg, Russia)
"Gaps in the continuous spectrum of periodic cylindrical waveguides".
The continuous spectrum of a waveguide of a straight cylindrical shape implies the semi-infinite segment [a,+infty) of the real axis in the complex plane. The continuous spectrum of a periodic waveguide can be of the gap-band structure, i.e. it is the union of infinite number of closed segments.
It will be demonstrated that by a proper but almost arbitrary small periodic perturbation of the boundary of a straight cylinder the continuous spectrum of the Dirichlet Laplacian gets a gap just after the first band. General formally self-adjoint elliptic problems, especially elasticity, will be discussed as well and the gaps will be constructed.