The Landis Conjecture For Nonlocal Elliptic Operators: Polynomial Decay

Abstract

We obtain a unique continuation result at infinity for fully nonlinear elliptic integro-differential operators of order 2s which satisfy the maximum and minimum principles in bounded subdomains, under the decay assumption $o(|x{|}^{-(N+2s)})$ at infinity. Our result is new even in the case of the fractional Laplacian, as it unveils the nonlocal nature of the decay in Landis conjecture, evolving from exponential to polynomial.

17 pages