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The existence question in the calculus of variations: a density result


Authors: Arrigo Cellina and Carlo Mariconda
Journal: Proc. Amer. Math. Soc. 120 (1994), 1145-1150
MSC: Primary 49J05
DOI: https://doi.org/10.1090/S0002-9939-1994-1174488-2
MathSciNet review: 1174488
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Abstract: We show the existence of a dense subset $ \mathcal{D}$ of $ \mathcal{C}(\mathbb{R})$ such that, for $ g$ in it, the problem

$\displaystyle {\text{minimum}}\;\int_0^T {g(x(t))dt + \int_0^T {h(x'(t))dt,\;x(0) = a,\;x(T) = b} } $

admits a solution for every lower semicontinuous $ h$ satisfying growth conditions

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1994-1174488-2
Keywords: Calculus of variations, subdifferential, relaxed problem, bipolar, Liapunov, measurable partition, equi--integrability
Article copyright: © Copyright 1994 American Mathematical Society

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