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Convexity of certain integrals of the calculus of variations

Published online by Cambridge University Press:  14 November 2011

B. Dacorogna
Affiliation:
Département de Mathématiques, Ecole Polytechnique Féderale, 1015 Lausanne, Switzerland

Synopsis

In this paper we study the convexity of the integral over the space . We isolate a necessary condition on f and we find necessary and sufficient conditions in the case where f(x, u, u′) = a(u)u′2n or g(u) + h(u′).

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1987

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References

1Ekeland, I. and Témam, R.. Analyse convexe et problèmes variationnels (Paris: Dunod, 1972).Google Scholar
2Hardy, G., Littlewood, J. and Polya, G.. Inequalities (Cambridge: Cambridge University Press, 1934).Google Scholar
3Marcellini, P. and Sbordone, C.. Semicontinuity problems in the calculus of variations. Nonlinear Anal. 4 (1980), 241257.CrossRefGoogle Scholar