Stability results for an inverse problem in potential theory (Q807779)

Let T be a bounded domain in \({\mathbb{R}}^ 2\) with \(C^{2,\lambda}\) boundary \((0<\lambda <1)\), let H be a domain such that \(\bar H\subset T\), and let \(\Gamma\) be a \(C^{3,\lambda}\) curve in H. This paper is concerned with stability results for an inverse problem which arises in electrocardiology. The problem is of the following form: given a function h defined on \(\partial T\), find \(\Gamma\) such that \(u_{\Gamma}\) (a function defined on \(T\setminus \Gamma\) in terms of an integral on \(\Gamma\)) agrees with h on \(\partial T\).