Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weak solutions for a stochastic mean curvature flow of two-dimensional
  graphs   We study a stochastically perturbed mean curvature flow for graphs in
$\mathbb{R}^3$ over the two-dimensional unit-cube subject to periodic boundary
conditions. In particular, we establish the existence of a weak martingale
solution. The proof is based on energy methods and therefore presents an
alternative to the stochastic viscosity solution approach. To overcome
difficulties induced by the degeneracy of the mean curvature operator and the
multiplicative gradient noise present in the model we employ a three step
approximation scheme together with refined stochastic compactness and
martingale identification methods.

29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con