Fully explicit quasiconvexification of the meansquare deviation of the gradient of the state in optimal design
Author:
Pablo Pedregal
Journal:
Electron. Res. Announc. Amer. Math. Soc. 7 (2001), 7278
MSC (2000):
Primary 49J45, 74P10
DOI:
https://doi.org/10.1090/S1079676201000968
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 meansquare 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 CastillaLa Mancha, 13071 Ciudad Real, Spain
Email:
ppedrega@indcr.uclm.es
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