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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  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  . 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