In this paper we establish in the fast diffusion range the higher integrability of the spatial gradient of weak solutions to porous medium systems. The result comes along with an explicit reverse Hölder inequality for the gradient. The novel feature in the proof is a suitable intrinsic scaling for space-time cylinders combined with reverse Hölder inequalities and a Vitali covering argument within this geometry. The main result holds for the natural range of parameters suggested by other regularity results. Our result applies to general fast diffusion systems and includes both, non-negative and signed solutions in the case of equations. The methods of proof are purely vectorial in their structure.

中文翻译：

---

单一多孔介质系统的更高集成度

在本文中，我们建立了在快速扩散范围内对多孔介质系统的弱解的空间梯度的更高可积性。结果伴随着梯度的显式逆霍勒不等式。证明中的新颖特征是适用于时空圆柱体的固有缩放比例，结合了反向Hölder不等式和此几何中的Vitali覆盖参数。主要结果保持其他规律性结果建议的参数的自然范围。我们的结果适用于一般的快速扩散系统，并且在方程式的情况下包括非负和有符号解。证明方法在结构上纯粹是矢量的。