Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic behavior of extremals for fractional Sobolev inequalities
  associated with singular problems   Let $\Omega$ be a smooth, bounded domain of $\mathbb{R}^{N}$, $\omega$ be a
positive, $L^{1}$-normalized function, and $0<s<1<p.$ We study the asymptotic
behavior, as $p\rightarrow\infty,$ of the pair $\left( \sqrt[p]{\Lambda_{p}%
},u_{p}\right) ,$ where $\Lambda_{p}$ is the best constant $C$ in the Sobolev
type inequality \[ C\exp\left( \int_{\Omega}(\log\left\vert u\right\vert
^{p})\omega \mathrm{d}x\right) \leq\left[ u\right] _{s,p}^{p}\quad\forall\,u\in
W_{0}^{s,p}(\Omega) \] and $u_{p}$ is the positive, suitably normalized
extremal function corresponding to $\Lambda_{p}$. We show that the limit pairs
are closely related to the problem of minimizing the quotient $\left\vert
u\right\vert _{s}/\exp\left( \int_{\Omega}(\log\left\vert u\right\vert )\omega
\mathrm{d}x\right) ,$ where $\left\vert u\right\vert _{s}$ denotes the
$s$-H\"{o}lder seminorm of a function $u\in C_{0}^{0,s}(\overline{\Omega}).$

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The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph