Structure of approximate solutions of variational problems with extended-valued convex integrands

Zaslavski, Alexander J.

ESAIM: Control, Optimisation and Calculus of Variations, Tome 15 (2009) no. 4, pp. 872-894.

In this work we study the structure of approximate solutions of autonomous variational problems with a lower semicontinuous strictly convex integrand $f$ : $R^n$$\times$$R^n$ $\to$ $R^1$$\cup$ $\left\{\infty \right\}$, where $R^n$ is the $n$-dimensional euclidean space. We obtain a full description of the structure of the approximate solutions which is independent of the length of the interval, for all sufficiently large intervals.

Classification : 49J99
Mots clés : good function, infinite horizon, integrand, overtaking optimal function, turnpike property

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