Spectral inequalities for Schrödinger equations with various potentials

2024/03/13 by Zhu, Jiuyi
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2403.08975

Abstract

We study the spectral inequalities of Schrödinger operator in the whole space for different potentials, which can be power growth or continuously vanishing at infinity. The spectral inequalities quantitatively depend on the density of the sensor sets with positive measure, growth rate of the potentials and spectrum (or eigenvalues). One important component in the poof is the adaptation of propagation of smallness argument for gradients in \citeLM18. As an application, we apply the spectral inequalities to obtain quantitative observability inequalities for heat equations.

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