An extension and trace theorem for functions of H-bounded variation in Carnot groups of step 2

2005/10/17 by Christina Selby, Selby, Christina · 1 citation
Biochemistry, Genetics and Molecular Biology · #22E25 #46E35 #Analysis of PDEs (math.AP) #Bone Metabolism and Diseases #Dermatological and Skeletal Disorders #FOS: Mathematics #Protein Tyrosine Phosphatases

paper · pdf · doi:10.48550/arxiv.math/0510350

openalex publication_date 2005/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper provides an extension for a function u ∈ BV_H(Ω) to a function u₀ ∈ BV_H(G) when Ω is ``H-admissible,'' and G is a step 2 Carnot group. It is shown that H-admissible domains include non-characteristic domains and domains in groups of Heisenberg type which have a partial symmetry about characteristic points. An example is given of a domain that is C^1,α, α<1, that is not H-admissible. Further, when Ω is H-admissible a trace theorem is proved for u ∈ BV_H(Ω).

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