This short note is concerned with a quasilinear diffusion equation under initial and Neumann boundary value condition. To be more precise, the authors establish a gradient maximum principle of classical solutions via the maximum principle and Hopf’s lemma. The result generalizes a recent work obtained by Kim (Proc Amer Math Soc 145:1203–1208, 2017).

中文翻译：

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拟线性抛物方程的解的最大梯度原理

此简短说明与初始和Neumann边界值条件下的拟线性扩散方程有关。更准确地说，作者通过极大值原理和霍普夫引理建立了经典解的梯度极大值原理。该结果概括了Kim最近获得的工作（Proc Amer Math Soc 145：1203-1208，2017）。