Stability for an inverse spectral problem of the biharmonic Schrödinger operator

Abstract

Let V be a bounded potential. We prove a Hölder stability estimate of determining the potential V from the boundary spectral data of the biharmonic operator Δ2+V. The boundary spectral data consists of the Dirichlet eigenvalues λk and the normal derivatives of the eigenfunctions ∂νϕk,∂νΔϕk on the boundary of a bounded domain. The analysis depends on the asymptotic behavior of the spectral data.