Volume 26, 2020
|Number of page(s)||27|
|Published online||08 September 2020|
A minimisation problem in L∞ with PDE and unilateral constraints*
Department of Mathematics and Statistics, University of Reading, Whiteknights,
PO Box 220,
RG6 6AX, UK.
** Corresponding author: firstname.lastname@example.org
Accepted: 29 April 2019
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.
Mathematics Subject Classification: 35Q93 / 49K20 / 49J40
Key words: Absolute minimisers / calculus of variations in L∞ / PDE-constrained optimisation / generalised Kuhn–Tucker theory / Lagrange multipliers / fluorescent optical tomography / Robin boundary conditions
© EDP Sciences, SMAI 2020
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.