TITLE

# From 1-homogeneous supremal functionals to difference quotients: relaxation and G-convergence

AUTHOR(S)
Garroni, Adriana; Ponsiglione, Marcello; Prinari, Francesca
PUB. DATE
December 2006
SOURCE
Calculus of Variations & Partial Differential Equations;Dec2006, Vol. 27 Issue 4, p397
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
In this paper we consider positively 1-homogeneous supremal functionals of the type F(u) := supO f (x,?u(x)). We prove that the relaxation ... is a difference quotient, that is ...(u) = RdF (u) := sup x,y?,O x ?y u(x) - u(y)/dF (x, y) for every u ? W1,8(O), where dF is a geodesic distance associated to F. Moreover we prove that the closure of the class of 1-homogeneous supremal functionals with respect to - convergence is given exactly by the class of difference quotients associated to geodesic distances. This class strictly contains supremal functionals, as the class of geodesic distances strictly contains intrinsic distances.
ACCESSION #
22478817

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