Preprint

Inserted: 17 aug 2025
Last Updated: 17 aug 2025

Year: 2025

Abstract:

We prove a new characterization of metric Sobolev spaces, in the spirit of Brezis-Van Schaftingen-Yung's asymptotic formula. A new feature of our work is that we do not need Poincar\'e inequality which is a common tool in the literature. Another new feature is that we find a direct link between Brezis-Van Schaftingen-Yung's asymptotic formula and Cheeger's Lipschitz differentiability.

Download:

• 20250423