Hopf's lemmas for parabolic fractional <i>p</i>-Laplacians
Pengyan Wang, Wenxiong Chen
Abstract
<p style='text-indent:20px;'>In this paper, we first establish Hopf's lemmas for parabolic fractional <inline-formula><tex-math id="M1">\begin{document}$ p $\end{document}</tex-math></inline-formula>-equations for <inline-formula><tex-math id="M2">\begin{document}$ p \geq 2 $\end{document}</tex-math></inline-formula>. Then we derive an asymptotic Hopf's lemma for anti-symmetric solutions to parabolic fractional Laplacians. We believe that these Hopf's lemmas will become powerful tools in obtaining qualitative properties of solutions for nonlocal parabolic equations.</p>
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