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