2000/08/31 by Nageswari Shanmugalingam · 740 citations
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Birnbaum–Orlicz space #Business #Computer science #Extension (predicate logic) #Functional analysis #Geometric Analysis and Curvature Flows #Interpolation space #Mathematics #Measure (data warehouse) #Metric (unit) #Metric space #Nonlinear Partial Differential Equations #Pure mathematics #Sobolev space
paper · pdf · doi:10.4171/rmi/275
published in Revista Matemática Iberoamericana 16(2), 243-279 (Royal Spanish Mathematical Society)
crossref issued 2000/08/31 · crossref published 2000/08/31 · crossref published-print 2000/08/31 · openalex publication_date 2000/08/31 · crossref created 2011/12/06 · openalex created_date 2025/10/10 · crossref deposited 2025/11/04 · openalex updated_date 2026/07/26 · crossref indexed 2026/08/06
This paper studies a possible definition of Sobolev spaces in abstract metric spaces and answers in the affirmative the question whether this definition yields a Banach space. The paper also explores the relationship between this definition and the Hajlasz spaces. For specialized metric spaces the Sobolev embedding theorems are proven. Different versions of capacities are also explored and these various definitions are compared. The main tool used in this paper is the concept of moduli of path families.