In this paper, we establish global boundedness and Hölder regularity of the weak solution to the following parabolic p(x,t)‐Laplace equation:

$$\begin{array}{ccc}\hfill & u_t-\text{div}\mathbf{a}(x,t,u,\nabla u)=b(x,t,u,\nabla u)\text{in}{Q}_T,\hfill & \hfill \\ \hfill & u(x,t)=0\text{on}\partial \mathrm{\Omega }\times (0,T),\hfill \\ \hfill & u(x,0)=u_0\text{in}\mathrm{\Omega },\hfill \end{array}$$

under some proper assumptions on a and b. The Hölder continuity given in the present work extends known results to the equation with a general nondivergence term.

中文翻译：

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一般p（x，t）-Laplace抛物方程的解的整体有界性和Hölder正则性

在本文中，我们建立了抛物线p（x，t）-Laplace方程的弱解的整体有界性和Hölder正则性：

$$\begin{array}{ccc}\hfill & {ü}_{Ť}-\text{div}\mathbf{一种}（X，Ť，ü，\nabla ü）=b（X，Ť，ü，\nabla ü）\text{在}{问}_{Ť}，\hfill & \hfill \\ \hfill & ü（X，Ť）=0\text{上}\partial \mathrm{\Omega }\times （0，Ť），\hfill \\ \hfill & ü（X，0）={ü}_0\text{在}\mathrm{\Omega }，\hfill \end{array}$$

在关于a和b的一些适当假设下。本工作中给出的Hölder连续性将已知结果扩展到具有一般非散度项的方程。