A minimisation problem in L∞ with PDE and unilateral constraints

Katzourakis, N. (2020) A minimisation problem in L∞ with PDE and unilateral constraints. ESAIM Control Optimization & Calculus of Variations, 26. 60. ISSN 1262-3377 doi: 10.1051/cocv/2019034

Abstract/Summary

We study the minimisation of a cost functional which measures the misfit on the boundary of a domain between a component of the solution to a certain parametric elliptic PDE system and a prediction of the values of this solution. We pose this problem as a PDE-constrained minimisation problem for a supremal cost functional in L∞, where except for the PDE constraint there is also a unilateral constraint on the parameter. We utilise approximation by PDE-constrained minimisation problems in Lp as p→∞ and the generalised Kuhn-Tucker theory to derive the relevant variational inequalities in Lp and L∞. These results are motivated by the mathematical modelling of the novel bio-medical imaging method of Fluorescent Optical Tomography.

Additional Information	The original publication is available at www.esaim-cocv.org
Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/83792
Identification Number/DOI	10.1051/cocv/2019034
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Additional Information	The original publication is available at www.esaim-cocv.org
Publisher	EDP Sciences
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