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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Remarks on quasiconvexity and stability of equilibria for variational integrals

Author: Kewei Zhang
Journal: Proc. Amer. Math. Soc. 114 (1992), 927-930
MSC: Primary 49K10
MathSciNet review: 1037211
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Abstract: Let $ F:{{\mathbf{R}}^{nN}} \to {\mathbf{R}}$ be a uniformly strictly quasiconvex function (see [3, 4]) of class $ {C^{2 + \alpha }},(0 < \alpha < 1)$, and be of polynomial growth. Then every smooth solution of the Euler-Lagrangian equation of the multiple integral $ I\left( {u;\Omega } \right) = {\smallint _\Omega }F(Du(x))dx$ is a minimum of $ I$ for variations of sufficiently small supports contained in $ \Omega $.

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PII: S 0002-9939(1992)1037211-6
Article copyright: © Copyright 1992 American Mathematical Society

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