Spectral inequality for Schrödinger equations with power growth potentials

2023/01/29 by Jiuyi Zhu, Zhu, Jiuyi, Jinping Zhuge +1 · 1 citation
Engineering · Mathematics · #35J10 #35P99 #47A11 #93B05 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2301.12338

openalex publication_date 2023/01/29 · openalex created_date 2023/02/02 · openalex updated_date 2026/07/28

Abstract

We prove a spectral inequality for Schrödinger equations with power growth potentials, which particularly confirms a conjecture in \citeDSV. 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.

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