Variational statement of an inverse problem for a domain (Q946109)

In this paper, a new variational approach is suggested for an inverse problem to determine a domain \(D\subset\mathbb R^r\) from Dirichlet and Neumann boundary data for the elliptic equation \(-\Delta u+au=f(x)\), where \(a\in C^1(\mathbb R^r)\) is a given positive function. The authors reduce this inverse problem to the minimization of a functional defined in \(D\), and provide an algorithm for numerical solution.