article

Title: Quantitative uniqueness for Schroedinger operator

Authors: Laurent Bakri

Issue: Volume 61 (2012), Issue 4, 1565-1580

Abstract:

$We give an upper bound on the vanishing order of solutions to Schr\"odinger's equation on a compact smooth manifold. Our method is based on Carleman type inequalities and gives a generalisation to a result of H. Donnelly and C. Fefferman [H. Donnelly and C. Fefferman, \textit{Nodal sets of eigenfunctions on Riemannian manifolds}, Invent. Math. \textbf{93} (1988), no. 1, 161--183] on eigenfunctions. It also sharpens previous results of I. Kukavica [I. Kukavica, \textit{Quantitative uniqueness for second-order elliptic operators}, Duke Math. J. \textbf{91} (1998), no. 2, 225--240].$