We derive conditional stability estimates for the Helmholtz type equations which are becoming of Lipschitz type for large frequencies/wave numbers. Proofs use splitting solutions into low and high frequencies parts where we use energy (in particular) Carleman estimates. We discuss numerical confirmation and open problems. We report on new stability estimates for recovery of the near field from the scattering amplitude and for Schroedinger potential from the Dirichlet-to Neumann map. In these estimates unstable (logarithmic part) goes to zero as the wave number grows. Proofs are using new bounds for Hankel functions and complex and real geometrical optics solutions.
Seminar on Analysis at University of Tsukuba