Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Moser functions and fractional Moser-Trudinger type inequalities   We improve the sharpness of some fractional Moser-Trudinger type
inequalities, particularly those studied by Lam-Lu and Martinazzi. As an
application, improving upon works of Adimurthi and Lakkis, we prove the
existence of weak solutions to the problem $(-\Delta)^\frac{n}{2}u=\lambda
ue^{bu^2} \,\text{ in }\Omega,\, 0<\lambda<\lambda_1,\,b>0,$ with Dirichlet
boundary condition, for any domain $\Omega$ in $\mathbb{R}^n$ with finite
measure. Here $\lambda_1$ is the first eigenvalue of $(-\Delta)^\frac n2$ on
$\Omega$.

9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat