THE ARONSON-BÉNILAN ESTIMATE IN LEBESGUE SPACES, GIULIA BEVILACQUA, BENOÎT PERTHAME, AND MARKUS SCHMIDTCHEN
03/08/2020ABSTRACT. In a celebrated three-pages long paper in 1979, Aronson and Bénilan obtained a re- markable 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 applica- tions 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 L^p spaces, of some modifications and improvements, as well as to show certain limitations of their strategy.
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