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Proceedings of the American Mathematical Society

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Local minimizers of integral functionals are global minimizers

Author: E. Giner
Journal: Proc. Amer. Math. Soc. 123 (1995), 755-757
MSC: Primary 49J10; Secondary 28B05, 49K10
MathSciNet review: 1254839
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Abstract: We show that local minimizers of integral functionals associated with a measurable integrand $ f:\Omega \times E \to \mathbb{R} \cup \{ \pm \infty \} $ are actually global minimizers. Here $ (\Omega, \mathcal{S},\mu )$ is a measured space with an atomless $ \sigma $-finite positive measure, E is a separable Banach space, and the integral functional $ {I_f}(x) = \smallint _\Omega ^ \ast f(\omega ,x(\omega ))d\mu $ is defined on $ {L_p}(\Omega ,E)$ or, more generally, on some decomposable set of measurable mappings x from $ \Omega $ into E.

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Keywords: Integral functional, measurable integrand, global optimization
Article copyright: © Copyright 1995 American Mathematical Society

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