Hopf's lemmas for parabolic fractional Laplacians and parabolic fractional $p$-Laplacians

Abstract

In this paper, we first establish Hopf's lemmas for parabolic fractional equations and parabolic fractional $p$-equations. Then we derive an asymptotic Hopf's lemma for antisymmetric solutions to parabolic fractional equations. We believe that these Hopf's lemmas will become powerful tools in obtaining qualitative properties of solutions for nonlocal parabolic equations.

References in corpus (1)

• A maximum principle on unbounded domains and a Liouville theorem for fractional p-harmonic functions

Cited by in corpus (1)

• Nonexistence of solutions for indefinite fractional parabolic equations