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Besov Estimates for Weak Solutions of the Parabolic p-Laplacian Equations
Bulletin of the Malaysian Mathematical Sciences Society ( IF 1.0 ) Pub Date : 2021-06-04 , DOI: 10.1007/s40840-021-01147-2
Rumeng Ma , Fengping Yao

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:

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\({\mathbf {F}}\) 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。

更新日期:2021-06-05
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