Sobolev and BV spaces on metric measure spaces via derivations and integration by parts

2014/09/19 by Simone Di Marino, Di Marino, Simone · 3 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG) #Nonlinear Partial Differential Equations #math.FA #math.MG

paper · pdf · doi:10.48550/arxiv.1409.5620

arXiv admin note: text overlap with arXiv:1111.3730 by other authors

arxiv created 2014/09/19 · openalex publication_date 2014/09/19 · arxiv updated 2014/09/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We develop a theory of BV and Sobolev Spaces via integration by parts formula in abstract metric spaces; the role of vector fields is played by Weaver's metric derivations. The definition hereby given is shown to be equivalent to many others present in literature.

Citations

• Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces

Cited by

• Preduals of metric BV spaces
• Spaces with Riemannian curvature bounds are universally infinitesimally Hilbertian
• Rectifiability of the reduced boundary for sets of finite perimeter over RCD(K,N) spaces

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