A remark on the direct method of the calculus of variations

J. P. Penot
1977 Proceedings of the American Mathematical Society  
This note deals with the problem of minimizing a real-valued function / on a weakly closed subset of a reflexive Banach space. We use a mild monotonicity assumption introduced by P. Hess [11] on the derivative /' of / to get the weak lower semicontinuity of /. We show that one can dispense with any continuity assumption on /', 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.
doi:10.1090/s0002-9939-1977-0464022-4 fatcat:zuu2mgyomngfxho5wdbytoqwau