An \(n\)-dimensional Borg--Levinson theorem for singular potentials
It is proved that the boundary spectral data, i.e. the Dirichlet eigenvalues and normal derivatives of the eigenfunctions at the boundary, determines uniquely the potential \(q\) in \(L^p\) for the Schrödinger equation \((-\Delta+ q)u= 0\) in a bounded domain \(\Omega\subset \mathbb{R}^n\), \(n\geq 2\), \(p> n/2\). This result generalizes the result of Nachman, Sylvester and Uhlmann to unbounded potentials and it can be viewed as an \(n\)-dimensional Borg-Levinson theorem.
scientific article; zbMATH DE number 1891076
scientific article