We study the parabolic fractional p−Laplace equation \ptu+(−Δp)su=0 in the degenerate range 2≤p<2/(1−s). We show that weak solutions are Lipschitz continuous in space and, if p>1/(1−s), also in time. We also prove a comparison principle for both weak and viscosity solutions, and establish the equivalence between the two notions of solution.
@article{arxiv.2603.12065,
title = {Fractional $p$-caloric functions are Lipschitz},
author = {David Jesus and Aelson Sobral and José Miguel Urbano},
journal= {arXiv preprint arXiv:2603.12065},
year = {2026}
}