Radial symmetry and Hopf lemma for fully nonlinear parabolic equations involving the fractional Laplacian

In this paper, we consider fully nonlinear parabolic problems involving the fractional Laplacian. Hopf type lemmas for both on bounded domain Ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varOmega $$\end{document} with smooth boundary and half space are obtained. When Ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varOmega $$\end{document} is a ball or the whole space, we obtain the radial symmetry results of positive solutions. Our results are an extension of Li-Nirenberg [19], Li-Chen [18] and Wang-Chen [24].