Carleman estimate for Zaremba boundary condition
Seminar Room 1, Newton Institute
The Zaremba boundary condition is a mixed boundary condition of the following type, on a part of the boundary we impose Dirichlet boundary condition and on the other part we impose the Neumann boundary condition. For such a problem we prove an logarithme type estimate for the decrease of energy of a solution for a damped wave equation. In the talk we shall explain the plan of the proof. The main part is to prove a Carleman estimate in a neighborhood of the boundary where the type of boundary conditions changes.