Laplace transform approach for an inverse problem

Abstract

In this paper we develop a Laplace transform method to solve an inverse problem associated with a boundary value problem in a domain with a simple geometry. The main ingredient in our approach is a vector-valued version of a Widder theorem (characterizing the Laplace transform of a bounded function).

We obtain the existence and uniqueness of a solution to the inverse problem. We also show a stability result in an appropriate sense.