Hölder gradient estimates for fractional $p$-caloric functions

Abstract

We establish interior $C^{1,\alpha }$ regularity estimates, for some $\alpha >0$, for fractional $p$-caloric functions when $p$ is in the range $p\in (2,2/(1-s))$. As a consequence, we deduce improved regularity in time, which yields interior continuous differentiability in time for $p\in [1/(1-s),2/(1-s))$.

arXiv comment35 pages, 1 figure