Identification of unbounded electric potentials through asymptotic boundary spectral data

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

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