Identification of unbounded electric potentials through asymptotic boundary spectral data

We prove that the real-valued electric potential q ∈ L^max (2,3 n /5)(Ω ) of the Dirichlet Laplacian -Δ +q acting in a bounded domain Ω⊂ℝ^n , n ≥ 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.