Geodesic
Fully explicit quasiconvexification of the mean-square deviation of the gradient of the state in optimal design
Pedregal, Pablo1
1 Departamento de Matemáticas, ETSI Industriales, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain
Electronic research announcements of the American Mathematical Society, Tome 07 (2001), pp. 72-78.

Voir la notice de l'article provenant de la source American Mathematical Society

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.
DOI : 10.1090/S1079-6762-01-00096-8

Pedregal, Pablo 1

1 Departamento de Matemáticas, ETSI Industriales, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain 
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Pedregal, Pablo. Fully explicit quasiconvexification of the mean-square deviation of the gradient of the state in optimal design. Electronic research announcements of the American Mathematical Society, Tome 07 (2001), pp. 72-78. doi : 10.1090/S1079-6762-01-00096-8. http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-01-00096-8/

[1] Dacorogna, Bernard Direct methods in the calculus of variations 1989

[2] Kohn, R. V. The relaxation of a double-well energy Contin. Mech. Thermodyn. 1991 193 236

[3] Bǎdescu, Radu On a problem of Goursat Gaz. Mat. 1939 571 577

[4] Murat, François Contre-exemples pour divers problèmes où le contrôle intervient dans les coefficients Ann. Mat. Pura Appl. (4) 1977 49 68

[5] Pedregal, Pablo Parametrized measures and variational principles 1997

[6] Šverák, Vladimír Lower-semicontinuity of variational integrals and compensated compactness 1995 1153 1158

[7] Calculus of variations, homogenization and continuum mechanics 1994

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