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Bourgain–Brezis–Mironescu Approach in Metric Spaces with Euclidean Tangents.

Authors :
Górny, Wojciech
Source :
Journal of Geometric Analysis; Apr2022, Vol. 32 Issue 4, p1-20, 20p
Publication Year :
2022

Abstract

In the setting of metric measure spaces satisfying the doubling condition and the (1, p)-Poincaré inequality, we prove a metric analogue of the Bourgain–Brezis–Mironescu formula for functions in the Sobolev space W 1 , p (X , d , ν) , under the assumption that for ν -a.e. point the tangent space in the Gromov–Hausdorff sense is Euclidean with fixed dimension N. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
10506926
Volume :
32
Issue :
4
Database :
Complementary Index
Journal :
Journal of Geometric Analysis
Publication Type :
Academic Journal
Accession number :
155071412
Full Text :
https://doi.org/10.1007/s12220-021-00861-4