New characterizations of Sobolev metric spaces
Simone Di Marino, Marco Squassina
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.
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.
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