In this paper, we study local uniform continuity of nonnegative weak solutions to degenerate diffusion-drift equations in the form of $u_t=\Delta u^m+\nabla \cdot \left(B(x,t)u\right),\text{for }m\ge 1$assuming a vector field $B\in L_t^p{L}_x^q$. Regarding local Hölder continuity, we provide a sharp condition on $p$ and $q$, which is referred to as the subcritical region. In the critical region, the divergence-free condition is essential to providing uniform continuity which depends on the modulus of continuity of the local norm of $B$.

中文翻译：

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退化扩散方程的连续性结果 ${升}_{吨}^{磷}{升}_X^q$ 漂移

在本文中，我们研究了退化扩散漂移方程的非负弱解的局部均匀连续性，其形式为 ${你}_{吨}=\Delta {你}^{米}+\nabla \cdot \left(乙(X,吨)你\right),\text{为了 }米\ge \mathrm{1个}$假设向量场 $乙\in {升}_{吨}^{磷}{升}_X^q$. 关于局部 Hölder 连续性，我们提供了一个尖锐的条件$磷$ 和 $q$，称为亚临界区。在临界区，无散度条件对于提供均匀连续性至关重要，这取决于局部范数的连续性模数$乙$.