# New characterizations of Sobolev metric spaces

## TL;DR

This paper introduces novel characterizations of Sobolev and BV spaces within doubling and Poincare metric spaces, extending classical limit formulas to more general metric settings.

## Contribution

It generalizes Bourgain-Brezis-Mironescu and Nguyen limit formulas to metric spaces, broadening the understanding of Sobolev and BV spaces beyond Euclidean domains.

## Key findings

- New characterizations of Sobolev and BV spaces in metric spaces
- Extension of classical limit formulas to non-Euclidean settings
- Broader applicability of Sobolev space theory

## Abstract

We provide new characterizations of Sobolev ad BV spaces in doubling and Poincare metric spaces in the spirit of the Bourgain-Brezis-Mironescu and Nguyen limit formulas holding in domains of R^N.