Sharp differentiability results for the lower local Lipschitz constant and applications to non-embedding

DOI10.1007/s12220-014-9527-9zbMath1339.26016OpenAlexW2091938189WikidataQ110233650 ScholiaQ110233650MaRDI QIDQ253827

Kevin Wildrick, Thomas Zürcher

Publication date: 8 March 2016

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

Full work available at URL: http://doc.rero.ch/record/332130/files/12220_2014_Article_9527.pdf

zbMATH Keywords

Sobolev spacedifferentiabilityembeddingLorentz spacePoincaré inequalityLipschitz property

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Metric spaces, metrizability (54E35) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Lipschitz (Hölder) classes (26A16) Special maps on metric spaces (54E40) Continuity and differentiation questions (26B05)

Related Items (4)

Absolutely continuous mappings on doubling metric measure spaces ⋮ N-Lusin property in metric measure spaces: a new sufficient condition ⋮ Mappings of finite distortion between metric measure spaces ⋮ On Stepanov type differentiability theorems

Cites Work

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• Compression bounds for Lipschitz maps from the Heisenberg group to \(L_{1}\)
• Extensions of Lipschitz maps into Banach spaces
• Space filling with metric measure spaces
• Editor's note: the differentiability of functions in \({\mathbb{R}}^ n\)
• Carnot-Carathéodory metrics and quasiisometries of symmetric spaces of rank 1
• Quasiconformal maps in metric spaces with controlled geometry
• Absolutely continuous functions of several variables
• Differentiability of Lipschitz functions on metric measure spaces
• Modulus and the Poincaré inequality on metric measure spaces
• Lectures on analysis on metric spaces
• Sobolev classes of Banach space-valued functions and quasiconformal mappings
• Extending Lipschitz functions via random metric partitions
• On functions with derivatives in a Lorentz space
• The Poincaré inequality for vector fields satisfying Hörmander's condition
• A differentiable structure for metric measure spaces
• Newtonian spaces: An extension of Sobolev spaces to metric measure spaces
• The Stepanov differentiability theorem in metric measure spaces
• Peano cubes with derivatives in a Lorentz space
• The Poincaré inequality is an open ended condition
• Local Lipschitz numbers and Sobolev spaces
• Differentiability of Lipschitz maps from metric measure spaces to Banach spaces with the Radon-Nikodym property
• Differentiable structures on metric spaces: A Primer
• Linear dilatation and differentiability of homeomorphisms of $\mathbb{R}^{n}$
• Fine behavior of functions whose gradients are in an Orlicz space
• Sobolev met Poincaré
• An embedding theorem for Sobolev type functions with gradients in a Lorentz space
• On the relationship between derivations and measurable differentiable structures
• Scaled-oscillation and regularity

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