We extend to the singular case the results in [El Bahja H. Regularity for anisotropic quasi-linear parabolic equations with variable growth. Electron J Differ Equ. 2019;2019(104):1–21] concerning the regularity of weak solutions of a class of anisotropic quasi-linear parabolic equations with variable exponents. The proof is based on DiBenedetto's technique called intrinsic scaling; by choosing an appropriate geometry one can deduce energy and logarithmic estimates from which one can implement an iterative method to obtain the regularity result.

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具有变量增长的奇异各向异性抛物线方程的局部连续性

我们将结果扩展到奇异情况 [El Bahja H. 具有可变增长的各向异性准线性抛物线方程的正则性。电子 J 差分方程。2019;2019(104):1-21] 关于一类变指数的各向异性拟线性抛物线方程弱解的规律性。该证明基于 DiBenedetto 的称为内在缩放的技术；通过选择合适的几何形状，人们可以推导出能量和对数估计，从中可以实施一种迭代方法来获得规律性结果。