A local uniqueness theorem for the fractional Schr\"{o}dinger equation on closed Riemannian manifolds

Yi-Hsuan Lin

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arXiv · 2409.01921

A local uniqueness theorem for the fractional Schr\"{o}dinger equation on closed Riemannian manifolds

Yi-Hsuan Lin

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Abstract

We investigate that a potential $V$ in the fractional Schr\"odinger equation $( (-\Delta_g )^s +V ) u=f$ can be recovered locally by using the local source-to-solution map on smooth connected closed Riemannian manifolds. To achieve this goal, we derive a related new Runge approximation property.

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Yi-Hsuan Lin. 2024-09-03. A local uniqueness theorem for the fractional Schr\"{o}dinger equation on closed Riemannian manifolds. https://arxiv.org/abs/2409.01921

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