Preprint 6/2005

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

Adriana Garroni, Marcello Ponsiglione, and Francesca Prinari

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Submission date: 13. Jan. 2005 (revised version: November 2005)
Pages: 23
published in: Calculus of variations and partial differential equations, 27 (2006) 4, p. 397-420 
DOI number (of the published article): 10.1007/s00526-005-0354-5
MSC-Numbers: 47J20, 58B20, 49J45
Keywords and phrases: variational methods, supremal functionals, finsler metric, relaxation, gamma convergence
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In this paper we consider positively 1-homogeneous supremal functionals of the type formula17. We prove that the relaxation formula19 is a difference quotient, that is
where formula23 is a geodesic distance associated to F. Moreover we prove that the closure of the class of 1-homogeneous supremal functionals with respect to formula29-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.

18.10.2019, 02:12