Spectral inequality for Schr\"odinger equations with power growth potentials
Analysis of PDEs
2023-01-31 v1
Abstract
We prove a spectral inequality for Schr\"odinger equations with power growth potentials, which particularly confirms a conjecture in \cite{DSV}. This spectral inequality depends on the decaying density of the sensor sets, and the growth rate of potentials. The proof relies on three-ball inequalities derived from modified versions of quantitative global and local Carleman estimates that take advantage of the gradient information of the potentials.
Keywords
Cite
@article{arxiv.2301.12338,
title = {Spectral inequality for Schr\"odinger equations with power growth potentials},
author = {Jiuyi Zhu and Jinping Zhuge},
journal= {arXiv preprint arXiv:2301.12338},
year = {2023}
}