Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A family of degenerate elliptic operators: maximum principle and its
  consequences   In this paper we investigate the validity and the consequences of the maximum
principle for degenerate elliptic operators whose higher order term is the sum
of "k" eigenvalues of the Hessian. In particular we shed some light on some
very unusual phenomena due to the degeneracy of the operator. We prove moreover
Lipschitz regularity results and boundary estimates for problems in convex
domains which are intersections of ball of same radius. We prove also that
smooth bounded strictly convex domains are part of this class. As a consequence
we obtain the existence of solutions of the Dirichlet problem and of principal
eigenfunctions.

31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th