Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Higher regularity estimates for the porous medium equation near the Heat
  equation   In this paper we investigate regularity aspects for solutions of the
nonlinear parabolic equation $$ u_t= \Delta u^m, \quad m > 1 $$ usually called
the porous medium equation. More precisely, we provide sharp regularity
estimates for bounded nonnegative weak solutions along the free boundary
$\partial\{u>0\}$, when the equation is universally close to the heat equation.
As a consequence, local Lipschitz estimates are also established for this
scenario.

3
The categories of this paper are: physics
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat