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Optimal L 1-Control in Coefficients for Dirichlet Elliptic Problems: W-Optimal Solutions

Author

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  • Peter I. Kogut

    (Dnipropetrovsk National University)

  • Guenter Leugering

    (Lehrstuhl II Universität Erlangen-Nürnberg)

Abstract

In this paper, we study a Dirichlet optimal control problem associated with a linear elliptic equation the coefficients of which we take as controls in the class of integrable functions. The coefficients may degenerate and, therefore, the problems may exhibit the so-called Lavrentieff phenomenon and non-uniqueness of weak solutions. We consider the solvability of this problem in the class of W-variational solutions. Using a concept of variational convergence of constrained minimization problems in variable spaces, we prove the existence of W-solutions to the optimal control problem and provide the way for their approximation. We emphasize that control problems of this type are important in material and topology optimization as well as in damage or life-cycle optimization.

Suggested Citation

  • Peter I. Kogut & Guenter Leugering, 2011. "Optimal L 1-Control in Coefficients for Dirichlet Elliptic Problems: W-Optimal Solutions," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 205-232, August.
    • Handle: RePEc:spr:joptap:v:150:y:2011:i:2:d:10.1007_s10957-011-9840-4
    DOI: 10.1007/s10957-011-9840-4
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    References listed on IDEAS

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    1. P. I. Kogut & G. Leugering, 2007. "Asymptotic Analysis of State Constrained Semilinear Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 135(2), pages 301-321, November.
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