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.

References in corpus (2)

• Asymptotic behavior of solutions of the stationary Navier-Stokes equations in an exterior domain
• A note on the boundedness of Riesz transform for some subelliptic operators