Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 $.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 49K10

Retrieve articles in all journals with MSC: 49K10


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1037211-6
PII: S 0002-9939(1992)1037211-6
Article copyright: © Copyright 1992 American Mathematical Society