Calculus of Variations and Geometric Measure Theory

C. Geldhauser - E. Valdinoci

Optimizing the fractional power in a model with stochastic PDE constraints

created by geldhause on 30 Mar 2017
modified on 09 Jun 2018



Inserted: 30 mar 2017
Last Updated: 9 jun 2018

Year: 2017


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.