We consider degenerate and singular parabolic equations with p-Laplacian structure in bounded nonsmooth domains when the right-hand side is a signed Radon measure with finite total mass. We develop a new tool that allows global regularity estimates for the spatial gradient of solutions to such parabolic measure data problems, by introducing the (intrinsic) fractional maximal function of a given measure.

中文翻译：

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涉及测度数据的退化/奇异抛物方程的整体正则性

当右侧是总质量有限的带符号Radon测度时，我们考虑在有界非光滑域中具有p -Laplacian结构的退化和奇异抛物方程。我们开发了一种新工具，通过引入给定度量的（本征）分数最大函数，可以对此类抛物线度量数据问题的解决方案的空间梯度进行全局正则估计。