Nonconvex Optimal Control and Variational Problems by Alexander J. Zaslavski

Author:Alexander J. Zaslavski
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

6. Nonoccurrence of the Lavrentiev Phenomenon for Variational Problems

Alexander J. Zaslavski1

(1)Department of Mathematics, Technion - Israel Institute of Technology, Haifa, Israel

Abstract

In this chapter we study nonoccurrence of the Lavrentiev phenomenon for a large class of nonconvex nonautonomous constrained variational problems. A state variable belongs to a convex subset H of a Banach space X with nonempty interior. Integrands belong to a complete metric space of functions which satisfy a growth condition common in the literature and are Lipschitzian on bounded sets. This space will be described below. In [97] we considered a class of nonconstrained variational problems with integrands belonging to a subset and showed that for the following property holds:

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