Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimizing the fractional power in a model with stochastic PDE
  constraints   We study an optimization problem with SPDE constraints, which has the
peculiarity that the control parameter $s$ is the $s$-th power of the diffusion
operator in the state equation. Well-posedness of the state equation and
differentiability properties with respect to the fractional parameter $s$ are
established. We show that under certain conditions on the noise, optimality
conditions for the control problem can be established.

5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph