On the fractional landis conjecture
In this paper we study a Landis-type conjecture for fractional Schr\"odinger equations of fractional power $s\in(0,1)$ with potentials. We discuss both the cases of differentiable and non-differentiable potentials. On the one hand, it turns out for \emph{differentiable} potentials with some a p...
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| Main Authors: | , |
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| Format: | Article (Journal) Chapter/Article |
| Language: | English |
| Published: |
12 Sept 2018
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| In: |
Arxiv
Year: 2018, Pages: 1-27 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: http://arxiv.org/abs/1809.04480
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| Author Notes: | Angkana Rüland and Jenn-Nan Wang |
| Summary: | In this paper we study a Landis-type conjecture for fractional Schr\"odinger equations of fractional power $s\in(0,1)$ with potentials. We discuss both the cases of differentiable and non-differentiable potentials. On the one hand, it turns out for \emph{differentiable} potentials with some a priori bounds, if a solution decays at a rate $e^{-|x|^{1+}}$, then this solution is trivial. On the other hand, for $s\in(1/4,1)$ and merely bounded \emph{non-differentiable} potentials, if a solution decays at a rate $e^{-|x|^\alpha}$ with $\alpha>4s/(4s-1)$, then this solution must again be trivial. Remark that when $s\to 1$, $4s/(4s-1)\to 4/3$ which is the optimal exponent for the standard Laplacian. For the case of non-differential potentials and $s\in(1/4,1)$, we also derive a quantitative estimate mimicking the classical result by Bourgain and Kenig. |
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| Item Description: | Gesehen am 12.05.2021 |
| Physical Description: | Online Resource |