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Functional Calculus
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Supremal Representation of L ∞ Functionals
Supremal Representation of L ∞ Functionals,10.1007/s0024500508216,Applied Mathematics and Optimization,Pierre Cardaliaguet,Francesca Prinari
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Supremal Representation of L ∞ Functionals
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Citations: 2
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Pierre Cardaliaguet
,
Francesca Prinari
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. 129141, 2005
DOI:
10.1007/s0024500508216
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Citation Context
(1)
...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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Citations
(2)
Semicontinuity and relaxation of L ∞ functionals
Francesca Prinari
Journal:
Advances in Calculus of Variations
, vol. 2, no. 1, pp. 4371, 2009
Semicontinuity and Supremal Representation in the Calculus of Variations
Francesca Prinari
Journal:
Applied Mathematics and Optimization  APPL MATH OPT
, vol. 58, no. 1, pp. 111145, 2008