Unique continuation for the Schrödinger equation with gradient term

Koh, Youngwoo; Seo, Ihyeok

doi:10.1090/proc/13942

Unique continuation for the Schrödinger equation with gradient term
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by Youngwoo Koh and Ihyeok Seo PDF

Proc. Amer. Math. Soc. 146 (2018), 2555-2562 Request permission

Abstract:

We obtain a unique continuation result for the differential inequality $| (i\partial _t +\Delta )u | \leq |Vu| + | W\cdot \nabla u |$ by establishing $L^2$ Carleman estimates. Here, $V$ is a scalar function and $W$ is a vector function, which may be time-dependent or time-independent. As a consequence, we give a similar result for the magnetic Schrödinger equation.

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