We consider viscosity solutions to non-homogeneous degenerate and singular parabolic equations of the $p$-Laplacian type and in non-divergence form. We provide local Hölder and Lipschitz estimates for the solutions. In the degenerate case, we prove the Hölder regularity of the gradient. Our study is based on a combination of the method of alternatives and the improvement of flatness estimates.

中文翻译：

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非散度型拟线性抛物方程的局部正则性

我们考虑非齐次退化的奇异抛物方程的粘性解 $p$-拉普拉斯型，且非散度形式。我们提供解决方案的本地Hölder和Lipschitz估算。在退化的情况下，我们证明了梯度的Hölder正则性。我们的研究基于替代方法和平面度估计值的改进。