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Zeitschrift für Analysis und ihre Anwendungen


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Volume 34, Issue 1, 2015, pp. 85–108
DOI: 10.4171/ZAA/1530

Published online: 2015-01-08

Optimal Control in Matrix-Valued Coefficients for Nonlinear Monotone Problems: Optimality Conditions I

Peter I. Kogut[1], Ol'ga P. Kupenko[2] and Günter Leugering[3]

(1) Dnipropetrovsk National University, Ukraine
(2) National Academy of Science of Ukraine, Kyiv, Ukraine
(3) Universität Erlangen-Nürnberg, Germany

In this article we study an optimal control problem for a nonlinear monotone Dirichlet problem where the controls are taken as matrix-valued coefficients in $L^\infty(\Omega;\mathbb{R}^{N\times N} )$. For the exemplary case of a tracking cost functional, we derive first order optimality conditions. This first part is concerned with the general case of matrix-valued coefficients under some hypothesis, while the second part focuses on the special class of diagonal matrices.

Keywords: Nonlinear monotone Dirichlet problem, control in coefficients, adjoint equation

Kogut Peter, Kupenko Ol'ga, Leugering Günter: Optimal Control in Matrix-Valued Coefficients for Nonlinear Monotone Problems: Optimality Conditions I. Z. Anal. Anwend. 34 (2015), 85-108. doi: 10.4171/ZAA/1530