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We explicitly compute the quasiconvexification of the resulting integrand associated with the mean-square deviation of the gradient of the state with respect to a given target field, when the underlying optimal design problem in conductivity is reformulated as a purely variational problem. What is remarkable, more than the formula itself, is the fact that it can be shown to be the full quasiconvexification.

Copyright 2001 American Mathematical Society

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Article Info

• ERA Amer. Math. Soc. 07 (2001), pp. 72-78
• Publisher Identifier: S 1079-6762(01)00096-8
• 2000 Mathematics Subject Classification. Primary 49J45, 74P10
• Received by the editors March 15, 2001
• Posted on August 22, 2001
• Communicated by Stuart Antman
• Comments (When Available)

Pablo Pedregal

Departamento de Matemáticas, ETSI Industriales, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain

E-mail address: ppedrega@ind-cr.uclm.es

I would like to acknowledge several stimulating conversations with R. Lipton concerning the type of optimal design problems considered here and to J. C. Bellido for carrying out various initial computations. I also appreciate the criticism of several referees which led to the improvement of several aspects of this note