Calculus of Variations and Geometric Measure Theory

E. Acerbi - G. Buttazzo - F. Prinari

The class of functionals which can be represented by a supremum

created on 02 Apr 2001
modified on 05 Dec 2002


Published Paper

Inserted: 2 apr 2001
Last Updated: 5 dec 2002

Journal: J. Convex Anal.
Volume: 9
Number: 1
Pages: 225-236
Year: 2002


We give a characterization of all lower semicontinuous functionals on $L^\infty_\mu$ which can be represented in the form $\mu-\sup\{f(x,u)\colon x\in A\}$. We also show by a counterexample that the representation above may fail if the lower semicontinuity condition is dropped.