Identification of unbounded electric potentials through asymptotic boundary spectral data

Abstract

We prove that the real-valued electric potential $q\in L^{\max (2,3n/5)}(\Omega )$ of the Dirichlet Laplacian $-\Delta +q$ acting in a bounded domain $\Omega \subset {\mathbb{R}}^n$, $n\ge 3$, is uniquely determined by the asymptotics of the eigenpairs formed by the eigenvalues and the boundary observation of the normal derivative of the eigenfunctions.