In this paper, we obtain the local regularity estimates in Besov spaces of weak solutions for the following parabolic p-Laplacian equations:

$$\begin{aligned} u_{t}-\text {div} ~\! a \left( Du, x,t \right) =\text {div}~ {\mathbf {F}} \end{aligned}$$

under some proper assumptions on the functions a and \({\mathbf {F}}\). Moreover, we would like to point out that our results improve the known results for such equations.

中文翻译：

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抛物线 p-拉普拉斯方程弱解的 Besov 估计

在本文中，我们获得了以下抛物线p- Laplacian 方程的弱解 Besov 空间中的局部正则性估计：

$$\begin{aligned} u_{t}-\text {div} ~\! a \left( Du, x,t \right) =\text {div}~ {\mathbf {F}} \end{aligned}$$

在对函数a和\({\mathbf {F}}\) 的一些适当假设下。此外，我们想指出，我们的结果改进了此类方程的已知结果。