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Fully explicit quasiconvexification of the mean-square deviation of the gradient of the state in optimal design
Author(s):
Pablo
Pedregal
Journal:
Electron. Res. Announc. Amer. Math. Soc.
7
(2001),
72-78.
MSC (2000):
Primary 49J45, 74P10
Posted:
August 22, 2001
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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.
References:
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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:
10.1090/S1079-6762-01-00096-8
PII:
S 1079-6762(01)00096-8
Received by editor(s):
March 15, 2001
Posted:
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
Copyright of article:
Copyright
2001,
American Mathematical Society
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