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arXiv · 1905.01885

On Landis Conjecture for the Fractional Schrödinger Equation

Pu-Zhao Kow
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Abstract

In this paper, we study a Landis-type conjecture for the general fractional Schrödinger equation $((-P)^{s}+q)u=0$. As a byproduct, we also proved the additivity and boundedness of the linear operator $(-P)^{s}$ for non-smooth coefficents. For differentiable potentials $q$, if a solution decays at a rate $\exp(-|x|^{1+})$, then the solution vanishes identically. For non-differentiable potentials $q$, if a solution decays at a rate $\exp(-|x|^{\frac{4s}{4s-1}+})$, then the solution must again be trivial. The proof relies on delicate Carleman estimates. This study is an extension of the work by Rüland-Wang (2019).

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Pu-Zhao Kow. 2021-11-22. On Landis Conjecture for the Fractional Schrödinger Equation. https://doi.org/10.4171/jst%2F433

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