Increased stability in the continuation of solutions to the Helmholtz equation

Abstract

In this paper we give analytical and numerical evidence of increasing stability in the Cauchy Problem for the Helmholtz equation when frequency is growing. This effect depends on convexity properties of the surface where the Cauchy Data are given. Proofs use Carleman estimates and the theory of elliptic boundary value problems in Sobolev spaces. Our numerical testing is handling the nearfield acoustical holography and it is based on the single layer representation algorithm.