Landis-type conjecture for the half-Laplacian
Abstract
In this paper, we study the Landis-type conjecture, i.e., unique continuation property from infinity, of the fractional Schrödinger 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.
- Publication:
-
arXiv e-prints
- Pub Date:
- June 2021
- DOI:
- 10.48550/arXiv.2106.06120
- arXiv:
- arXiv:2106.06120
- Bibcode:
- 2021arXiv210606120K
- Keywords:
-
- Mathematics - Analysis of PDEs;
- Primary: 35A02;
- 35B40;
- 35R11. Secondary: 35J05;
- 35J15
- E-Print:
- doi:10.1090/proc/16093