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

TL;DR

This paper proves a strong-type unique continuation principle for the fractional p-Laplacian operator, extending to solutions of the fractional nonlinear Schrödinger equation, using a simplified proof approach.

Contribution

It introduces a straightforward proof of the strong UCP for the fractional p-Laplacian, expanding its applicability to nonlinear Schrödinger equations.

Findings

Established a strong-type UCP for fractional p-Laplacian

Extended the result to fractional nonlinear Schrödinger solutions

Simplified the proof method based on recent weak UCP proofs

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 Schr\"odinger equation. We adapt the recent proofs of the weak UCP by Berger, Schilling and Prasad.