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| Volume 7, Number 1, April 2006, pp. 51-66 | |||||||||
| Alexander J. Zaslavski | |||||||||
| Key words: | |||||||||
| Banach space, integrand, Lavrentiev phenomenon, variational problem | |||||||||
| Mathematices Subject Classification: 49J27 | |||||||||
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| Volume 7, Number 1, April 2006, pp. 51-66 | |||||||||
| Alexander J. Zaslavski | |||||||||
| Key words: | |||||||||
| Banach space, integrand, Lavrentiev phenomenon, variational problem | |||||||||
| Mathematices Subject Classification: 49J27 | |||||||||
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| Abstract: | |||
| In this paper we study nonoccurrence of the Lavrentiev phenomenon for a large class of nonautonomous constrained variational problems with a state variable which belongs to a convex subset of a Banach space with nonempty interior. In our previous work [15] we considered a class of nonconvex nonautonomous constrained variational problems with integrands belonging to a a complete metric space of functions $\mathcal M$ which satisfy a growth condition common in the literature and are Lipschitzian on bounded sets. In [15] we established nonoccurrence of the Lavrentiev phenomenon for most elements of $\mathcal M$ in the sense of Baire category. In this paper we show nonoccurrence of the Lavrentiev phenomenon for most elements of a subset of $\mathcal M$ consisting of all integrands which are convex with respect to the last variable (derivative). |
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| Nonoccurrence of the Lavrentiev phenomenon for many convex variational problems in Banach spaces | ||