Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Full and partial regularity for a class of nonlinear free boundary
  problems   In this paper we classify the nonnegative global minimizers of the functional
\[ J_F(u)=\int_\Omega F(|\nabla u|^2)+\lambda^2\chi_{\{u>0\}}, \] where $F$
satisfies some structural conditions and $\chi_D$ is the characteristic
function of a set $D\subset \mathbb R^n$. We compute the second variation of
the energy and study the properties of the stability operator. The free
boundary $\partial\{u>0\}$ can be seen as a rectifiable $n-1$ varifold. If the
free boundary is a Lipschitz multigraph then we show that the first variation
of this varifold is bounded and use Allard's monotonicity formula to prove the
existence of tangent cones modulo a set of small Hausdorff dimension. In
particular we prove that if $n=3$ and the ellipticity constants of the
quasilinear elliptic operator generated by $F$ are close to 1 then the conical
free boundary must be flat.

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The categories of this paper are: hep-ph
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph