Besov Estimates for Weak Solutions of the Parabolic p-Laplacian Equations

In this paper, we obtain the local regularity estimates in Besov spaces of weak solutions for the following parabolic p-Laplacian equations: ut-divaDu,x,t=divF\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} u_{t}-\text {div} ~\! a \left( Du, x,t \right) =\text {div}~ {\mathbf {F}} \end{aligned}$$\end{document}under some proper assumptions on the functions a and F\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf {F}}$$\end{document}. Moreover, we would like to point out that our results improve the known results for such equations.