The Stepanov differentiability theorem in metric measure spaces

DOI10.1007/BF02922098zbMath1069.28001OpenAlexW1972911574MaRDI QIDQ1886943

Kevin Rogovin, Thomas Zürcher, Zoltán M. Balogh

Publication date: 23 November 2004

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02922098

zbMATH Keywords

differentiabilitymetric spacePoincaré inequalitySobolev function

Mathematics Subject Classification ID

Length, area, volume, other geometric measure theory (28A75) Continuity and differentiation questions (26B05) Abstract differentiation theory, differentiation of set functions (28A15)

Related Items (13)

Nonsmooth calculus ⋮ Cheeger-différentiabilité d'applications de certains espaces de Sobolev ⋮ Differentiability of \(p\)-harmonic functions on metric measure spaces ⋮ Thin Loewner Carpets and Their Quasisymmetric Embeddings in S² ⋮ Space filling with metric measure spaces ⋮ Integral energy characterization of Hajłasz-Sobolev spaces ⋮ Dilatation, pointwise Lipschitz constants, and condition \(N\) on curves ⋮ Scaled-oscillation and regularity ⋮ Pointwise Lipschitz functions on metric spaces ⋮ Mappings of finite distortion from generalized manifolds ⋮ Aspects of area formulas by way of Luzin, Radó, and Reichelderfer on metric measure spaces ⋮ Sharp differentiability results for the lower local Lipschitz constant and applications to non-embedding ⋮ Derivations and Alberti representations

Cites Work

• Quasiconformal maps in metric spaces with controlled geometry
• A simple proof of the Stepanov theorem on differentiability almost everywhere
• Differentiability of Lipschitz functions on metric measure spaces
• Axiomatic theory of Sobolev spaces
• Lectures on analysis on metric spaces
• Definitions of Sobolev classes on metric spaces
• A differentiable structure for metric measure spaces
• Newtonian spaces: An extension of Sobolev spaces to metric measure spaces
• Sobolev spaces on an arbitrary metric space
• Lectures on \(n\)-dimensional quasiconformal mappings
• Maximal functions measuring smoothness
• Sobolev met Poincaré
• Measurable differentiable structures and the Poincare inequality
• Scaled-oscillation and regularity
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