Landis-type conjecture for the half-Laplacian
Analysis of PDEs
2023-04-14 v2
Abstract
In this paper, we study the Landis-type conjecture, i.e., unique continuation property from infinity, of the fractional Schr\"{o}dinger equation with drift and potential terms. We show that if any solution of the equation decays at a certain exponential rate, then it must be trivial. The main ingredients of our proof are the Caffarelli-Silvestre extension and Armitage's Liouville-type theorem.
Keywords
Cite
@article{arxiv.2106.06120,
title = {Landis-type conjecture for the half-Laplacian},
author = {Pu-Zhao Kow and Jenn-Nan Wang},
journal= {arXiv preprint arXiv:2106.06120},
year = {2023}
}