Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Strong solutions of semilinear parabolic equations with measure data and
  generalized backward stochastic differential equations   We prove that under natural assumptions on the data strong solutions in
Sobolev spaces of semilinear parabolic equations in divergence form involving
measure on the right-hand side may be represented by solutions of some
generalized backward stochastic differential equations. As an application we
provide stochastic representation of strong solutions of the obstacle problem
be means of solutions of some reflected backward stochastic differential
equations. To prove the latter result we use a stochastic homographic
approximation for solutions of the reflected backward equation. The
approximation may be viewed as a stochastic analogue of the homographic
approximation for solutions to the obstacle problem.

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The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph