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Landis-type conjecture for the half-Laplacian
Journal
Proceedings of the American Mathematical Society
Journal Volume
151
Journal Issue
7
End Page
2962
Date Issued
2021-06-11
Author(s)
Pu-Zhao Kow
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.
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.
Subjects
Caarelli- Silvestre extension | half-Laplacian | Landis conjecture | Liouville-type theorem | Unique continuation property; Mathematics - Analysis of PDEs; Mathematics - Analysis of PDEs; Primary: 35A02, 35B40, 35R11. Secondary: 35J05, 35J15
Type
journal article