A unique-continuation-at-infinity result in the analysis of partial differential equations, extending the Landis conjecture to fully nonlinear nonlocal elliptic integro-differential operators of order 2s (including the fractional Laplacian). It shows that a viscosity solution of Iu + Vu = 0 on R^N that decays faster than |x|^{-(N+2s)} at infinity must be identically zero, so the critical decay threshold forcing triviality is polynomial for nonlocal operators rather than the exponential threshold of the classical local case. Students learn how a nonlocal weak Harnack inequality, adapted to carry a zero-order term, yields a lower polynomial decay bound for positive supersolutions on arbitrarily large balls, and how the maximum and minimum principles in bounded subdomains close the argument.
A research note in the analysis of partial differential equations establishing a version of the Landis conjecture (a unique-continuation-at-infinity principle) for fully nonlinear nonlocal elliptic i…