# Optimizing the fractional power in a model with stochastic PDE constraints

created by geldhause on 30 Mar 2017

[BibTeX]

Preprint

Inserted: 30 mar 2017
Last Updated: 30 mar 2017

Year: 2017

Abstract:

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.