Journal of Convex Analysis 12 (2005), No. 1, 113--130
Copyright Heldermann Verlag 2005
On the Relaxation of a Class of Functionals Defined on Riemannian Distances
Andrea Davini
Dip. di Matematica, Università di Pisa, via Buonarroti 2, 56127 Pisa, Italy
davini@dm.unipi.it
We study the relaxation of a class of functionals defined on distances induced by isotropic Riemannian metrics on an open subset of RN. We prove that isotropic Riemannian metrics are dense in Finsler ones and we show that the relaxed functionals admit a specific integral representation.
Keywords: Riemannian and Finsler metrics, relaxation, Gamma convergence.
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