Sharp Vanishing order of solutions to Stationary Schrodinger equations on Carnot groups of arbitrary step

Abstract

Based on a variant of the frequency function approach of Almgren([Al]), we establish an optimal upper bound on the vanishing order of solutions to stationary Schrödinger equations associated to sub-Laplacian on Carnot groups of arbitrary step. Such bound provides a quantitative form of strong unique continuation and can be thought of as an analogue of the recent results of Bakri and Zhu for the standard Laplacian.

arXiv commentrevised version, accepted for publication in Journal of Mathematical Analysis and Applications