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

Florian Grube

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

Analysis of PDEs 2026-04-29 v2

Authors: Florian Grube

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.

Keywords

Unique continuation Fractional Laplacian $p$-Laplacian Nonlinear Schrödinger equation Partial differential equations

Cite

@article{arxiv.2604.18571,
  title  = {A strong-type unique continuation principle for the fractional $p$-Laplacian},
  author = {Florian Grube},
  journal= {arXiv preprint arXiv:2604.18571},
  year   = {2026}
}

Comments

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

Related papers

View all related →