We give a characterization of all lower semicontinuous functionals on Lm¥ which can be represented in the form m-sup{ f(x, u): x from A }. We also show by a counterexample that the representation above may fail if the lower semicontinuity condition is dropped.
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EA
Emilio Acerbi
Dip. di Matematica, Università di Parma, Via D'Azeglio 85/A, 43100 Parma, Italy
E. Acerbi, G. Buttazzo, F. Prinari. “The Class of Functionals which can be Represented by a Supremum.” Journal of Convex Analysis 9 (2002), No. 1, 225–236.