Calculus of Variations and Geometric Measure Theory

A. Davini

On the relaxation of a class of functionals defined on Riemannian distances

created on 05 Mar 2003
modified by davini on 13 Jul 2023

[BibTeX]

Published Paper

Inserted: 5 mar 2003
Last Updated: 13 jul 2023

Journal: J. Convex Anal.
Volume: 12
Number: 1
Pages: 113–130
Year: 2005

Abstract:

In this paper we study the relaxation of a class of functionals defined on distances induced by isotropic Riemannian metrics on an open subset of $\mathbb{R}^N$. We prove that isotropic Riemannian metrics are dense in Finsler ones and we show that the relaxed functionals admit a specific integral representation.

Keywords: relaxation, Gamma convergence, Finsler metrics, Riemannian metrics


Download: