Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Liouville-type results in two dimensions for stationary points of
  functionals with linear growth   We consider variational integrals of linear growth satisfying the condition
of $\mu$-ellipticity for some exponent $\mu >1$ and prove that stationary
points $u$: $\mathbb{R}^2 \to \mathbb{R}^N$ with the property \[
\limsup_{|x|\to \infty} \frac{|u(x)|}{|x|} < \infty \] must be affine
functions. The latter condition can be dropped in the scalar case together with
appropriate assumptions on the energy density providing an extension of
Bernstein's theorem.

11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc