On the Nash point equilibria in the calculus of variations (Q919257)

The paper refers to some recent contributions on the existence and the regularity of local minima in the calculus of variations. The purpose of the paper is to extend results of \textit{E. Acerbi} and \textit{N. Fusco} [Arch. Ration. Mech. Anal. 86, 125-145 (1984; Zbl 0565.49010)] and of \textit{M. Giaquinta} and \textit{E. Giusti} [Acta Math. 148, 31-46 (1982; Zbl 0494.49031)] concerning local minima and saddle points to Nash point equilibria for variational integrals. The same problems have been studied by \textit{A. Bensoussan} and \textit{J. Frehse} [see Nonlinear analysis and optimization, Proc. Int. Conf., Bologna/Italy 1982, Lect. Notes Math. 1107, 28-62 (1984; Zbl 0567.35006)]. The main difference in this paper is the author's assumption on quasi- convexity which replaces an ellipticity condition in the paper of Bensoussan and Frehse. This approach makes the argument clearer and more direct, and the theorems may be applied to a large class of functions.