This work extends monotonicity-based methods in inverse problems to the case of the Helmholtz (or stationary Schrödinger) equation for fixed non-resonance frequency and real-valued scattering coefficient function. We show a new monotonicity relation between the scattering coefficient and the local Neumann-Dirichlet operator that holds up to finitely many eigenvalues. Combining this with the method of localized potentials, we derive a new local uniqueness result, and a constructive monotonicity-based characterization of scatterers from partial boundary data.

This presentation is part of Minisymposium “MS1 - Inverse scattering and electrical impedance tomography (2 parts)”
organized by: Nuutti Hyvönen (Aalto University) , Roland Griesmaier (Karlsruhe Institute of Technology) .

Authors:

Bastian Harrach (Goethe-Universität Frankfurt am Main)

Mikko Salo (University of Jyväskylä)

Valter Pohjola (University of Jyväskylä)

Keywords:

helmholtz equation, inverse problems, inverse scattering, monotonicity method, partial differential equation models