Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The structure of the singular set in the thin obstacle problem for
  degenerate parabolic equations   We study the singular set in the thin obstacle problem for degenerate
parabolic equations with weight $|y|^a$ for $a \in (-1,1)$. Such problem arises
as the local extension of the obstacle problem for the fractional heat operator
$(\partial_t - \Delta_x)^s$ for $s \in (0,1)$. Our main result establishes the
complete structure and regularity of the singular set of the free boundary. To
achieve it, we prove Almgren-Poon, Weiss, and Monneau type monotonicity
formulas which generalize those for the case of the heat equation ($a=0$).

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The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
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The categories of this paper are: eess
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an