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Semicontinuous envelopes of polyconvex integrals

Published online by Cambridge University Press:  14 November 2011

Emilio Acerbi  and
Giuseppe Buttazzo
Emilio Acerbi
Affiliation:
Scuola Normale, p. Cavalieri 7, Pisa, Italy
Giuseppe Buttazzo
Affiliation:
Scuola Normale, p. Cavalieri 7, Pisa, Italy
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Synopsis

We answer some questions about the semicontinuity in L∞ and in Lp of functionals defined on W1,n (Ωℝn) as integrals of non-convex functions of the gradient matrix, and we give a conjecture for the general case.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 96 , Issue 1-2 , 1984 , pp. 51 - 54
Copyright
Copyright © Royal Society of Edinburgh 1984

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References

1Acerbi, E., Buttazzo, G. and Fusco, N.. Semicontinuity and relaxation for integrals depending on vector-valued functions. J. Math. Pures Appl., to appear.Google Scholar
2Marcellini, P. and Sbordone, C.. Semicontinuity problems in the calculus of variations. Nonlinear Anal. 4 (1980), 241–257.CrossRefGoogle Scholar
3Morrey, C. B.. Multiple integrals in the calculus of variations (Berlin: Springer, 1966).CrossRefGoogle Scholar