Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Subelliptic Analogue of Aronson-Serrin's Harnack Inequality   We show that the Harnack inequality for a class of degenerate parabolic
quasilinear PDE $$\p_t u=-X_i^* A_i(x,t,u,Xu)+ B(x,t,u,Xu),$$ associated to a
system of Lipschitz continuous vector fields $X=(X_1,...,X_m)$ in in $\Om\times
(0,T)$ with $\Om \subset M$ an open subset of a manifold $M$ with control
metric $d$ corresponding to $X$ and a measure $d\sigma$ follows from the basic
hypothesis of doubling condition and a weak Poincar\'e inequality. We also show
that such hypothesis hold for a class of Riemannian metrics $g_\e$ collapsing
to a sub-Riemannian metric $\lim_{\e\to 0} g_\e=g_0$ uniformly in the parameter
$\e\ge 0$.

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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: nlin
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The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th