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We investigate that a potential V  in the fractional Schrödinger equation \(\left ( \left ( -\varDelta _g \right )^s +V \right ) u=f\) 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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A Local Uniqueness Theorem for the Fractional Schrödinger Equation on Closed Riemannian Manifolds

  • 会议论文

  • 发表日期：

    2025年

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  • Yi-Hsuan Lin

摘要

We investigate that a potential V  in the fractional Schrödinger equation \(\left ( \left ( -\varDelta _g \right )^s +V \right ) u=f\) 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.