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

Author: Pablo Pedregal
Journal: Electron. Res. Announc. Amer. Math. Soc. 7 (2001), 72-78
MSC (2000): Primary 49J45, 74P10
Published electronically: August 22, 2001
MathSciNet review: 1856792
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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.

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Additional Information

Pablo Pedregal
Affiliation: Departamento de Matemáticas, ETSI Industriales, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain

Received by editor(s): March 15, 2001
Published electronically: August 22, 2001
Additional Notes: 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.
Communicated by: Stuart Antman
Article copyright: © Copyright 2001 American Mathematical Society