Uniqueness theorems for inverse obstacle scattering in Lipschitz domains

TL;DR

This paper introduces a new method to prove uniqueness in inverse obstacle scattering problems within Lipschitz domains, avoiding reliance on spectral discreteness and leveraging the separability of Hilbert spaces.

Contribution

It develops a novel proof technique for uniqueness in inverse scattering that does not depend on the spectrum's discreteness, expanding theoretical understanding.

Findings

Established uniqueness results for inverse obstacle scattering in Lipschitz domains

Developed a new proof method independent of spectral discreteness

Utilized Hilbert space separability in the proof

Abstract

An inverse problem of finding an obstacle and the boundary condition on its surface from the fixed-energy scattering data is studied. A new method is developed for a proof of the uniqueness results. The method does not use the discreteness of the spectrum of the corresponding Laplacian in a bounded domain. Proof of the uniqueness results is based on the fact that the Hilbert space of square integrable functions is separable.