Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a class of elliptic free boundary problems with multiple solutions   We prove that a certain class of elliptic free boundary problems, which
includes the Prandtl-Batchelor problem from fluid dynamics as a special case,
has two distinct nontrivial solutions for large values of a parameter. The
first solution is a global minimizer of the energy. The energy functional is
nondifferentiable, so standard variational arguments cannot be used directly to
obtain a second nontrivial solution. We obtain our second solution as the limit
of mountain pass points of a sequence of $C^1$-functionals approximating the
energy. We use careful estimates of the corresponding energy levels to show
that this limit is neither trivial nor a minimizer.

11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org