Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Singular Behavior of the Solution to the Stochastic Heat Equation on a
  Polygonal Domain   We study the stochastic heat equation with trace class noise and zero
Dirichlet boundary condition on a bounded polygonal domain O in R^2. It is
shown that the solution u can be decomposed into a regular part u_R and a
singular part u_S which incorporates the corner singularity functions for the
Poisson problem. Due to the temporal irregularity of the noise, both u_R and
u_S have negative L_2-Sobolev regularity of order s<-1/2 in time. The regular
part u_R admits spatial Sobolev regularity of order r=2, while the spatial
Sobolev regularity of u_S is restricted by r<1+\pi/\gamma, where \gamma is the
largest interior angle at the boundary of O. We obtain estimates for the
Sobolev norm of u_R and the Sobolev norms of the coefficients of the
singularity functions. The proof is based on a Laplace transform argument
w.r.t. the time variable. The result is of interest in the context of numerical
methods for stochastic PDEs.

1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex