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Convexity of certain integrals of the calculus of variations

Published online by Cambridge University Press:  14 November 2011

B. Dacorogna
B. Dacorogna
Affiliation:
Département de Mathématiques, Ecole Polytechnique Féderale, 1015 Lausanne, Switzerland
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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
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 107 , Issue 1-2 , 1987 , pp. 15 - 26
Copyright
Copyright © Royal Society of Edinburgh 1987

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References

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3Marcellini, P. and Sbordone, C.. Semicontinuity problems in the calculus of variations. Nonlinear Anal. 4 (1980), 241–257.CrossRefGoogle Scholar