Lipschitz stability for an inverse source scattering problem at a fixed frequency

TL;DR

This paper establishes Lipschitz stability for an inverse source problem in 3D Helmholtz equation using a single boundary measurement at a fixed frequency, assuming the source is piecewise constant on a union of convex polyhedral subdomains.

Contribution

It demonstrates Lipschitz stability for the inverse source problem under piecewise constant source assumptions, a novel result in this context.

Findings

Lipschitz stability is achieved for the inverse source problem.

Stability holds with a single boundary measurement at fixed frequency.

The source function is assumed to be piecewise constant on convex polyhedral subdomains.

Abstract

This paper is concerned with an inverse source problem for the three-dimensional Helmholtz equation by a single boundary measurement at a fixed frequency. We show the Lipschitz stability under the assumption that the source function is piecewise constant on a domain which is made of a union of disjoint convex polyhedral subdomains..