A remark on the direct method of the calculus of variations

Penot, J. P.

doi:10.1090/S0002-9939-1977-0464022-4

A remark on the direct method of the calculus of variations
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Proc. Amer. Math. Soc. 67 (1977), 135-141 Request permission

Abstract:

This note deals with the problem of minimizing a real-valued function f on a weakly closed subset of a reflexive Banach space. We use a mild monotonicity assumption introduced by P. Hess [11] on the derivative f’ of f to get the weak lower semicontinuity of f. We show that one can dispense with any continuity assumption on f’, so that we get a true generalization of F. E. Browder’s results [4]. The relevance of the monotonicity property to the calculus of variations is shown by an example.

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Sur la dualité et la sensibilité dans les problèmes de programmation mathématique

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