On an inverse Robin spectral problem

We consider the problem of the recovery of a Robin coefficient on a part gamma subset of partial differential omega of the boundary of a bounded domain omega from the principal eigenvalue and the boundary values of the normal derivative of the principal eigenfunction of the Laplace operator with Dirichlet boundary condition on partial differential omega\gamma. We prove the uniqueness, as well as local Lipschitz stability of the inverse problem. Moreover, we present an iterative reconstruction algorithm with numerical computations in two dimensions showing the accuracy of the method.