Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Best Constant, the Nonexistence of Extremal Functions and Related
  Results for an Improved Hardy-Sobolev Inequality   We present the best constant and the existence of extremal functions for an
Improved Hardy-Sobolev inequality. We prove that, under a proper
transformation, this inequality is equivalent to the Sobolev inequality in
$\mathbb{R}^N$. We also discuss the connection of the related functional spaces
and as a result we obtain some Caffarelli - Kohn - Nirenberg inequalities. Our
starting point is the existence of a minimizer for the Bliss' inequality and
the indirect dependence of the Hardy inequality at the origin.

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The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
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The categories of this paper are: supr-con
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys