On the uniqueness of variable coefficient Schrödinger equations

Author:

Federico Serena1ORCID,Li Zongyuan2ORCID,Yu Xueying34ORCID

Affiliation:

1. Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato 5, 40126 Bologna, Italy

2. Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong SAR

3. Department of Mathematics, Oregon State University, Kidder Hall 368, Corvallis, OR 97331, USA

4. Department of Mathematics, University of Washington, C138 Padelford Hall, Box 354350, Seattle, WA 98195, USA

Abstract

In this paper, we prove unique continuation properties for linear variable coefficient Schrödinger equations with bounded real potentials. Under certain smallness conditions on the leading coefficients, we prove that solutions decaying faster than any cubic exponential rate at two different times must be identically zero. Assuming a transversally anisotropic type condition, we recover the sharp Gaussian (quadratic exponential) rate in the series of works by Escauriaza–Kenig–Ponce–Vega [On uniqueness properties of solutions of Schrödinger equations, Comm. Partial Differential Equations 31(10–12) (2006) 1811–1823; Hardy’s uncertainty principle, convexity and Schrödinger evolutions, J. Eur. Math. Soc. (JEMS) 10(4) (2008) 883–907; The sharp Hardy uncertainty principle for Schrödinger evolutions, Duke Math. J. 155(1) (2010) 163–187].

Funder

AMS-Simons travel grant

Rutgers University

Institute for Computational and Experimental Research in Mathematics in Providence

Publisher

World Scientific Pub Co Pte Ltd

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Carleman estimates for third order operators of KdV and non KdV-type and applications;Annali di Matematica Pura ed Applicata (1923 -);2024-06-04

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