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Explicit quasiconvexification for some cost functionals depending on derivatives of the state in optimal designing

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  • We study relaxation for optimal design problems in conductivity in the two-dimensional situation. To this end, we reformulate the optimal design problem in an equivalent way as a genuine vector variational problem, and then analyze relaxation of this new variational problem. Our main achievement is to explicitly compute the quasiconvexification of the involved density in this problem for some interesting cases. We think the method given here could be generalized to compute quasiconvex envelopes in other situations. We restrict attention to the two-dimensional case.
    Mathematics Subject Classification: 49J45, 74P10.


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