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

DOI:
https://doi.org/10.1090/S1079-6762-01-00096-8

Published electronically:
August 22, 2001

MathSciNet review:
1856792

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Abstract | References | Similar Articles | Additional Information

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

Email:
ppedrega@ind-cr.uclm.es

DOI:
https://doi.org/10.1090/S1079-6762-01-00096-8

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