Abstract In this paper, we show that solutions of u t − div ( m | u | m − 1 ∇ u ) = f ∈ L q , r , m > 1 , are locally of class C 0 , γ with γ = min ⁡ { ν α 0 − , ( 2 q − n ) r − 2 q q [ m r − ( m − 1 ) ] } , where α 0 denotes the optimal Holder exponent for solutions of the homogeneous case and ν = 2 ( 2 + ( m − 1 ) α 0 ) − 1 . This improves the recent result of Araujo, Maia, Urbano [1] . For the Porous Medium Equation, unlike other known examples, the main difficulty is that the θ-parabolic geometry of the equation and the available regularity do not match. Despite this difficulty, considering γ as a function of m, our regularity result and the optimal local regularity of the associated homogeneous equation are comparable.

中文翻译：

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改进非均匀多孔介质方程的规律性

摘要 在本文中，我们证明了 ut − div ( m | u | m − 1 ∇ u )= f ∈ L q , r , m > 1 的解是 C 0 , γ 类的局部解，其中 γ = min ⁡ { ν α 0 − , ( 2 q − n ) r − 2 qq [ mr − ( m − 1 ) ] } ，其中 α 0 表示齐次情况下的最优 Holder 指数，ν = 2 ( 2 + ( m − 1 ) α 0 ) − 1 。这改善了 Araujo、Maia、Urbano [1] 最近的结果。对于多孔介质方程，与其他已知示例不同，主要困难在于方程的 θ-抛物线几何与可用的正则性不匹配。尽管有这个困难，考虑到 γ 作为 m 的函数，我们的正则性结果和相关齐次方程的最优局部正则性是可比的。