Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sharp capacity estimates in s-John domains   It is well-known that several problems related to analysis on $s$-John
domains can be unified by certain capacity lower estimates. In this paper, we
obtain general lower bounds of $p$-capacity of a compact set $E$ and the
central Whitney cube $Q_0$ in terms of the Hausdorff $q$-content of $E$ in an
$s$-John domain $\Omega$. Moreover, we construct several examples to show the
essential sharpness of our estimates.

7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin