# On the Lower Semicontinuity of Supremal Functionals

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 9, page 135-143
- ISSN: 1292-8119

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topGori, Michele, and Maggi, Francesco. "On the Lower Semicontinuity of Supremal Functionals." ESAIM: Control, Optimisation and Calculus of Variations 9 (2010): 135-143. <http://eudml.org/doc/90685>.

@article{Gori2010,

abstract = {
In this paper we study the lower semicontinuity problem for a supremal
functional of the form $F(u,\Omega )= \underset\{x\in\Omega\}\{\rm ess\,sup\} f(x,u(x),Du(x))$
with respect to the strong convergence in L∞(Ω),
furnishing a comparison with the analogous theory developed by
Serrin for integrals. A sort of Mazur's lemma for gradients of uniformly
converging sequences is proved.
},

author = {Gori, Michele, Maggi, Francesco},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = { Supremal functionals; lower semicontinuity;
level convexity; Calculus of Variations; Mazur's lemma.; supremal functionals; level convexity; Mazur lemma},

language = {eng},

month = {3},

pages = {135-143},

publisher = {EDP Sciences},

title = {On the Lower Semicontinuity of Supremal Functionals},

url = {http://eudml.org/doc/90685},

volume = {9},

year = {2010},

}

TY - JOUR

AU - Gori, Michele

AU - Maggi, Francesco

TI - On the Lower Semicontinuity of Supremal Functionals

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

PB - EDP Sciences

VL - 9

SP - 135

EP - 143

AB -
In this paper we study the lower semicontinuity problem for a supremal
functional of the form $F(u,\Omega )= \underset{x\in\Omega}{\rm ess\,sup} f(x,u(x),Du(x))$
with respect to the strong convergence in L∞(Ω),
furnishing a comparison with the analogous theory developed by
Serrin for integrals. A sort of Mazur's lemma for gradients of uniformly
converging sequences is proved.

LA - eng

KW - Supremal functionals; lower semicontinuity;
level convexity; Calculus of Variations; Mazur's lemma.; supremal functionals; level convexity; Mazur lemma

UR - http://eudml.org/doc/90685

ER -

## References

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