Recovering point sources for the inhomogeneous Helmholtz equation*The work of GB is supported in part by a NSFC Innovative Group Fund (No. 11621101). The work of FT is supported in part by the Grant ANR-17-CE40-0029 of the French National Research Agency ANR (project MultiOnde). (5th August 2021) - Bao, Gang; Liu, Yuantong; Triki, Faouzi
Abstract: The paper is concerned with an inverse point source problem for the Helmholtz equation. It consists of recovering the locations and amplitudes of a finite number of radiative point sources inside a given inhomogeneous medium from the knowledge of a single boundary measurement. The main result of the paper is a new Hölder type stability estimate for the inversion under the assumption that the point sources are well separated. The proof of the stability is based on a combination of Carleman estimates and a technique for proving uniqueness of the Cauchy problem.