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Supremal Representation of L ∞ Functionals

Supremal Representation of L ∞ Functionals,10.1007/s00245-005-0821-6,Applied Mathematics and Optimization,Pierre Cardaliaguet,Francesca Prinari

Supremal Representation of L ∞ Functionals   (Citations: 2)
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We characterize the maps F=F(u,A) defined for u ∈ W1,∞ and A open, which can be written as supremal functionals of the form F(u,A)=ess supx ∈ A f(x,u(x),Du(x)).
Journal: Applied Mathematics and Optimization - APPL MATH OPT , vol. 52, no. 2, pp. 129-141, 2005
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    • ...In the choice of a suitable supremand we have been inspired by the one constructed in [8] (see Theorem 2.2 and Lemma 3.4 therein)...
    • ...1 of [8], if F is a supremal functional of the form (2.9), it is not possible to represent F through the function h defined by...
    • ...The following proof is inspired by the proof of Lemma 3.3 in [8]...
    • ...We underline the difference between the following theorem and the representation result shown in Theorem 2.2 in [8]...

    Francesca Prinari. Semicontinuity and Supremal Representation in the Calculus of Variatio...

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