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Differentiability properties of the minimal average action. (English) Zbl 0835.58013
The paper studies the minimal average action for a variational problem on the \((n + 1)\)-torus under the Legendre and some growth conditions for the integrand. The minimization of the variational integral is considered with respect to compactly supported variations. Among other things the author gives a necessary and sufficient condition for the differentiability of the minimal average action \(A(\alpha)\) at an arbitrary rotation vector \(\alpha \in \mathbb{R}^n\). The study of the minimal average action is motivated from solid state physics.
Reviewer: D.Motreanu (Iaşi)

MSC:
58E30 Variational principles in infinite-dimensional spaces
46G05 Derivatives of functions in infinite-dimensional spaces
26B25 Convexity of real functions of several variables, generalizations
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