Calculus of Variations and Geometric Measure Theory

A. Davini

Smooth approximation of weak Finsler metrics

created on 29 Jan 2004
modified by davini on 25 Oct 2005


Published Paper

Inserted: 29 jan 2004
Last Updated: 25 oct 2005

Journal: Adv. Differential Equations
Volume: 18
Number: 8
Pages: 509-530
Year: 2005


Smooth Finsler metrics are a natural generalization of Riemannian ones and have been widely studied in the framework of differential geometry. The definition can be weakened by allowing the metric to be only Borel measurable. This generalization is necessary in view of applications, such as, for instance, optimization problems. In this paper we show that smooth Finsler metrics are dense in Borel ones, generalizing some results already obtained in a previous work. The case of degenerate Finsler distances is also discussed.