The author presents a simplified proof for the local continuity of the weak solutions to the porous medium equation with variable positive bounded exponent \(\gamma (x,t)\)

$$\begin{aligned} u_t-\nabla \cdot \left( |u|^{\gamma (x,t)} \, \nabla u\right) =0 , \quad \mathrm {in} \quad \Omega _T =\Omega \times (0,T] , 0<T<\infty . \end{aligned}$$

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中文翻译：

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再谈变指数多孔介质方程

作者提供了具有可变正界指数\（\ gamma（x，t）\）的多孔介质方程弱解的局部连续性的简化证明

$$ \ begin {aligned} u_t- \ nabla \ cdot \ left（| u | ^ {\ gamma（x，t）} \，\ nabla u \ right）= 0，\ quad \ mathrm {in} \ quad \ Ω_T = \Ω\ times（0，T]，0 <T <\ infty。\ end {aligned} $$

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