A strong-type unique continuation principle for the fractional $p$-Laplacian

Abstract

We provide a simple and direct proof of a strong-type unique continuation principle for the fractional $p$-Laplacian $(-{\Delta }_p{)}^s$ for a range of $s$ and $p$. The result extends to strong solutions of the fractional nonlinear Schrödinger equation. We adapt the recent proofs of the weak UCP by Berger, Schilling and Prasad.

9 pages; fixed error in the proof; this requires stronger assumptions