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arXiv · 1703.09329

Optimizing the fractional power in a model with stochastic PDE constraints

Carina Geldhauser·Enrico Valdinoci
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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.

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Carina Geldhauser, Enrico Valdinoci. 2017-03-27. Optimizing the fractional power in a model with stochastic PDE constraints. https://arxiv.org/abs/1703.09329

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