Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On $p$-modulus estimates in Orlicz-Sobolev classes   Under a condition of the Calderon type on $\varphi$, we show that a
homeomorphism $f$ of finite distortion in $W^{1,\varphi}_{\rm loc}$ and, in
particular, $f\in W^{1,q}_{\rm loc}$ for $q>n-1$ in ${\Bbb R}^n$, $n\ge 3$, is
a lower $Q$-homeomorphisms with respect to the $p$-modulus with $\left[
K_{I,\alpha}(x,f)\right]^{\beta}$, $p>n-1$ and a ring $Q_{*}$-homeomorphism
with respect to the $\frac{p}{p-n+1}$-modulus with $Q_{*}(x)=K_{I,\alpha}(x,f)$
where $ K_{I,\alpha}(x,f)$ is its inner $\alpha$-dilatation and
$\alpha=\frac{p}{p-n+1}$, $\beta=\frac{p-n+1}{n-1}$.

36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex