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Fully explicit quasiconvexification of the mean-square deviation of the gradient of the state in optimal design
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## Fully explicit quasiconvexification of the mean-square deviation of the gradient of the state in optimal design

### Pablo Pedregal

**Abstract.**
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

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