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Zeitschrift für Analysis und ihre Anwendungen


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Volume 34, Issue 2, 2015, pp. 199–219
DOI: 10.4171/ZAA/1536

Published online: 2015-04-08

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

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 paper we study an optimal control problem for a nonlinear monotone Dirichlet problem where the controls are taken as the matrix-valued coefficients in $L^{\infty}(\Omega; \mathbb R^{N \times N})$. Given a suitable cost function, the objective is to provide a substantiation of the first order optimality conditions using the concept of convergence in variable spaces. While in the rst part [Z. Anal. Anwend. 34 (2015), 85–108] optimality conditions have been derived and analysed in the general case under some assumptions on the quasi-adjoint states, in this second part, we consider diagonal matrices and analyse the corresponding optimality system without such assumptions.

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

Kogut Peter, Kupenko Ol'ga, Leugering Günter: Optimal Control in Matrix-Valued Coefficients for Nonlinear Monotone Problems: Optimality Conditions II. Z. Anal. Anwend. 34 (2015), 199-219. doi: 10.4171/ZAA/1536