Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the exterior Dirichlet problem for Hessian equations   In this paper, we establish a theorem on the existence of the solutions of
the exterior Dirichlet problem for Hessian equations with prescribed asymptotic
behavior at infinity. This extends a result of Caffarelli and Li for the
Monge-Amp\`{e}re equation to Hessian equations.

3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn