Metric Sobolev spaces. I: Equivalence of definitions

DOI10.1007/S00032-024-00407-7MaRDI QIDQ6655896

Toni Ikonen, Enrico Pasqualetto, Danka Lučić, Luigi Ambrosio

Publication date: 27 December 2024

Published in: Milan Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

Sobolev spacecapacitydivergenceDirichlet spacebarycenterderivationmetric measure spaceLipschitz functionmodulusplan of curves

Mathematics Subject Classification ID

Contents, measures, outer measures, capacities (28A12) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Applications of functional analysis in optimization, convex analysis, mathematical programming, economics (46N10) Banach spaces of continuous, differentiable or analytic functions (46E15) Potentials and capacities on other spaces (31C15) Absolutely continuous real functions in one variable (26A46)

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