## Title data

Clason, Christian ; Schiela, Anton:

**Optimal control of elliptic equations with positive measures.**

Universität Duisburg-Essen; Universität Bayreuth

*In:* Control, Optimisation and Calculus of Variations.
(2015)
.
- 30 S..

ISSN 1262-3377

DOI: https://doi.org/10.1051/cocv/2015046

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## Abstract in another language

Optimal control problems without control costs in general do not possess solutions due to the lack of coercivity. However, unilateral constraints together with the assumption of existence of strictly positive solutions of a pre-adjoint state equation, are sufficient to obtain existence of optimal solutions in the space of Radon measures. Optimality conditions for these generalized minimizers can be obtained using Fenchel duality, which requires a non-standard perturbation approach if the control-to-observation mapping is not continuous (e.g., for Neumann boundary control in three dimensions). Combining a conforming discretization of the measure space with a semismooth Newton method allows the numerical solution of the optimal control problem.