Quantitative uniqueness of continuation for the Schr\"odinger equation : explicit dependence on the potential

Abstract

We demonstrate a quantitative version of the usual properties related to unique continuation from an interior datum for the Schr\"odinger equation with bounded or unbounded potential. The inequalities we establish have constants that explicitly depend on the potential. We also indicate how the above-mentioned inequalities can be extended to elliptic equations with bounded or unbounded first-order derivatives. The case of unique continuation from Cauchy data is also considered.