Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Harnack inequality for a class of nonlocal parabolic equations   In this paper we establish a scale invariant Harnack inequality for the
fractional powers of parabolic operators $(\partial_t - \mathscr{L})^s$,
$0<s<1$, where $\mathscr{L}$ is the infinitesimal generator of a class of
symmetric semigroups. As a by-product we also obtain a similar result for the
nonlocal operators $(-\mathscr{L})^s$. Our focus is on non-Euclidean
situations.

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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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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
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The categories of this paper are: stat
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The categories of this paper are: chem-ph
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The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int