Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multiple solutions for some strongly degenerate second order elliptic
  equations   We consider a boundary value problem in a bounded domain involving a
degenerate operator of the form $$L(u)=-\textrm{div} (a(x)\nabla u)$$ and a
suitable nonlinearity $f$. The function $a$ vanishes on smooth 1-codimensional
submanifolds of $\Omega$ where it is not allowed to be $C^{2}$. By using
weighted Sobolev spaces we are still able to find existence of solutions which
vanish, in the trace sense, on the set where $a$ vanishes.

34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol