Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Aronson-B\'enilan Estimate in Lebesgue Spaces   In a celebrated three-pages long paper in 1979, Aronson and B\'enilan
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
B\'enilan estimate in Lp spaces, of some modifications and improvements, as
well as to show certain limitations of their strategy.

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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ph
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
3
The categories of this paper are: physics
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The categories of this paper are: stat