JournalszaaVol. 34, No. 2pp. 199–219

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

  • Peter I. Kogut

    Dnipropetrovsk National University, Ukraine
  • Ol'ga P. Kupenko

    National Academy of Science of Ukraine, Kyiv, Ukraine
  • Günter Leugering

    Universität Erlangen-Nürnberg, Germany
Optimal Control in Matrix-Valued Coefficients for Nonlinear Monotone Problems: Optimality Conditions II cover
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Abstract

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(Ω;RN×N)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.

Cite this article

Peter I. Kogut, Ol'ga P. Kupenko, Günter Leugering, Optimal Control in Matrix-Valued Coefficients for Nonlinear Monotone Problems: Optimality Conditions II. Z. Anal. Anwend. 34 (2015), no. 2, pp. 199–219

DOI 10.4171/ZAA/1536