Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: H\"older regularity of the Boltzmann equation past an obstacle   Regularity and singularity of the solutions according to the shape of domains
is a challenging research theme in the Boltzmann theory (\cite{Kim11,GKTT1}).
In this paper, we prove an optimal H\"older regularity in
$C^{0,\frac{1}{2}-}_{x,v}$ for the Boltzmann equation of the hard-sphere
molecule, which undergoes the elastic reflection in the intermolecular
collision and the contact with the boundary of a convex obstacle. In
particular, this H\"older regularity result is a stark contrast to the case of
other physical boundary conditions (such as the diffuse reflection boundary
condition and in-flow boundary condition), for which the solutions of the
Boltzmann equation develop discontinuity in a codimension 1 subset
(\cite{Kim11}), and therefore the best possible regularity is BV, which has
been proved in \cite{GKTT2}.

18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th