Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the lack of compactness in the 2D critical Sobolev embedding   This paper is devoted to the description of the lack of compactness of
$H^1_{rad}(\R^2)$ in the Orlicz space. Our result is expressed in terms of the
concentration-type examples derived by P. -L. Lions. The approach that we adopt
to establish this characterization is completely different from the methods
used in the study of the lack of compactness of Sobolev embedding in Lebesgue
spaces and take into account the variational aspect of Orlicz spaces. We also
investigate the feature of the solutions of non linear wave equation with
exponential growth, where the Orlicz norm plays a decisive role.

30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex