Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Compactness and existence results for degenerate critical elliptic
  equations   This paper is devoted to the study of degenerate critical elliptic equations
of Caffarelli-Kohn-Nirenberg type. By means of blow-up analysis techniques, we
prove an a-priori estimate in a weighted space of continuous functions. From
this compactness result, the existence of a solution to our problem is proved
by exploiting the homotopy invariance of the Leray-Schauder degree.

29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
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
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con