On the fractional Landis conjecture
In this paper we study a Landis-type conjecture for fractional Schrödinger equations of fractional power s∈(0,1) with potentials. We discuss both the cases of differentiable and non-differentiable potentials. On the one hand, it turns out for differentiable potentials with some a priori bounds, if...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article (Journal) |
| Language: | English |
| Published: |
7 June 2019
|
| In: |
Journal of functional analysis
Year: 2019, Volume: 277, Issue: 9, Pages: 3236-3270 |
| ISSN: | 1096-0783 |
| DOI: | 10.1016/j.jfa.2019.05.026 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1016/j.jfa.2019.05.026 Verlag, lizenzpflichtig, Volltext: https://www.sciencedirect.com/science/article/pii/S0022123619302022 
|
| Author Notes: | Angkana Rüland, Jenn-Nan Wang |
| Summary: | In this paper we study a Landis-type conjecture for fractional Schrödinger equations of fractional power s∈(0,1) with potentials. We discuss both the cases of differentiable and non-differentiable potentials. On the one hand, it turns out for 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∈(1/4,1) and merely bounded non-differentiable potentials, if a solution decays at a rate e−|x|α with α>4s/(4s−1), then this solution must again be trivial. Remark that when s→1, 4s/(4s−1)→4/3 which is the optimal exponent for the standard Laplacian. For the case of non-differentiable potentials and s∈(1/4,1), we also derive a quantitative estimate mimicking the classical result by Bourgain and Kenig. |
|---|---|
| Item Description: | Gesehen am 12.05.2021 |
| Physical Description: | Online Resource |
| ISSN: | 1096-0783 |
| DOI: | 10.1016/j.jfa.2019.05.026 |