# American Institute of Mathematical Sciences

November  2002, 8(4): 967-982. doi: 10.3934/dcds.2002.8.967

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

 1 Departamento de Matemáticas, Universidad de Castilla-La Mancha, c/ Campus Universitario s.n., 13.071-Ciudad Real, Spain 2 E.T.S. Ingenieros Industriales, Universidad de Castilla La Mancha, Spain

Received  April 2001 Revised  May 2002 Published  July 2002

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.
Citation: José C. Bellido, Pablo Pedregal. Explicit quasiconvexification for some cost functionals depending on derivatives of the state in optimal designing. Discrete & Continuous Dynamical Systems - A, 2002, 8 (4) : 967-982. doi: 10.3934/dcds.2002.8.967
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