Nonoccurrence of the Lavrentiev Phenomenon for Variational Problems

Alexander J. Zaslavski
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Alexander J. Zaslavski: Technion - Israel Institute of Technology

Chapter Chapter 6 in Nonconvex Optimal Control and Variational Problems, 2013, pp 159-195 from Springer

Abstract: 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 $$\mathcal{M}_{B}$$ 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 $$\mathcal{L}_{B} \subset \mathcal{M}_{B}$$ and showed that for $$f \in \mathcal{L}_{B}$$ the following property holds:

Keywords: Lavrentiev Phenomenon; Constrained Variational Problem; Lipschitz Solution; Integrable Scalar Function; Baire Category (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4614-7378-7_6

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DOI: 10.1007/978-1-4614-7378-7_6

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