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Weierstrass condition for the general basic variational problem

Published online by Cambridge University Press:  14 November 2011

Farhad Hüsseinov
Farhad Hüsseinov
Affiliation:
Bilkent University, Department of Economics, 06533, Ankara, Turkey
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Abstract

The Weierstrass necessary condition for a multidimensional basic variational problem due to Hadamard is strengthened.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 125 , Issue 4 , 1995 , pp. 801 - 806
Copyright
Copyright © Royal Society of Edinburgh 1995

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References

1Ball, J. M.. Existence theorems in nonlinear elasticity. Arch. Rational Mech. Anal 63 (1977), 337–403.CrossRefGoogle Scholar
2Bogolubov, N. N.. Sur quelques methods novelles dans le calculus des variations. Ann. Math. Pura Appl. (4) 7(1930), 249–71.CrossRefGoogle Scholar
3Dacorogna, B.. Quasiconvexity and relaxation for nonconvex problems in the calculus of variations. J. Fund. Anal. 46 (1982), 102–18.CrossRefGoogle Scholar
4Dacorogna, B.. Direct Methods in the Calculus of Variations (Berlin: Springer, 1989).CrossRefGoogle Scholar
5Evans, L. C.. Quasiconvexity and partial regularity in the calculus of variations. Arch. Rational Mech. Anal. 95(1986), 227–52.Google Scholar
6Gamkrelidze, R. V.. Foundations of Optimal Control (Tbilisi: Tbilisi University Press, 1975).Google Scholar
7Graves, L. M.. The Weierstrass condition for multiple integral variation problems. Duke Math. J. 5 (1939), 656–60.CrossRefGoogle Scholar
8Hüsseinov, F. V. (Guseinov, F. V.). Lower semicontinuous extension of the fundamental problem of calculus of variations. Mat. Zametki 45 (3) (1989), 43–52; English translation: Math. Notes 45 (3) (1989), 210–17.Google Scholar
9Hadamard, J.. Sur une question de calcul des variations. Bull. Soc. Math. France 30 (1902), 253–6.Google Scholar
10Hadamard, J.. Leçons sur la Propagation des Ondes (Paris: Hermann, 1903).Google Scholar
11Hüsseinov, F. V.. Continuity of quasiconvex functions and theorem on quasiconvexification. Izv. Akad. Nauk Azerbaidzhan. SSR Ser. Fiz.-Tekhn. Mat. Nauk 8 (1988), 17–23.Google Scholar
12Ioffe, A. D. and Tikhomirov, V. M.. Theory of Extremal Problems (Moscow: Nauka, 1974).Google Scholar
13Morrey, Ch. B.. Quasiconvexity and the lower semi-continuity of multiple integrals. Pacific J. Math. 2 (1952), 25–53.CrossRefGoogle Scholar
14Morrey, Ch. B.. Multiple Integrals in the Calculus of Variations (Berlin: Springer, 1966).CrossRefGoogle Scholar
15Sverak, V.. Rank-one convexity does not imply quasiconvexity. Proc. Roy. Soc. Edinburgh Sect. A (1992), 185–9.CrossRefGoogle Scholar