Lebesgue空间中的Aronson-Bénilan估计
The Aronson-Bénilan Estimate in Lebesgue Spaces
摘要：
在一个著名的三页长的文件在1979年，阿伦森和Bénilan获得了显着的估计二阶导数的解决方案的多孔介质方程。多孔介质渗流理论自发表以来，在热力学、气体流动、地下水流以及生态种群动力学等方面得到了广泛的应用。本文的目的是澄清最近在Lp空间中推广的Aronson和Bénilan估计的使用，一些修改和改进，以及显示其策略的某些限制。
英文摘要：
In a celebrated three-pages long paper in 1979, Aronson and Bénilan obtained a remarkable estimate on second order derivatives for the solution of the porous media equation. Since its publication, the theory of porous medium flow has expanded relentlessly with applications including thermodynamics, gas flow, ground water flow as well as ecological population dynamics. The purpose of this paper is to clarify the use of recent extensions of the Aronson and Bénilan estimate in Lp spaces, of some modifications and improvements, as well as to show certain limitations of their strategy.
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