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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, UniversitÓ di Pisa, via Buonarroti 2, 56127 Pisa, Italy

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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