# Reconstruction of a source domain from the Cauchy data

## TL;DR

This paper presents a method to reconstruct the shape of a polygonal source support in a Helmholtz equation from boundary Cauchy data, advancing inverse boundary value problem techniques.

## Contribution

It introduces a way to compute the support function of polygonal sources using boundary data, providing a new approach for inverse source reconstruction.

## Key findings

- Support function can be calculated from boundary Cauchy data for polygonal shapes.
- Method applies to inverse boundary value problems involving Helmholtz equations.
- Reconstruction is feasible for polygonal supports, aiding inverse problem solutions.

## Abstract

We consider an inverse source problem for the Helmholtz equation in a bounded domain. The problem is to reconstruct the shape of the support of a source term from the Cauchy data on the boundary of the solution of the governing equation. We prove that if the shape is a polygon, one can calculate its support function from such data. An application to the inverse boundary value problem is also included.