Hölder continuity of the traces of Sobolev functions to hypersurfaces in Carnot groups and the \(\mathcal{P} \)-differentiability of Sobolev mappings

DOI10.1134/s0037446623040043zbMath1530.46032MaRDI QIDQ6175220

Sergei Vodop'yanov, Unnamed Author

Publication date: 18 August 2023

Published in: Siberian Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

Sobolev spacesCarnot groupquasiconformal analysis

Mathematics Subject Classification ID

Quasiconformal mappings in (mathbb{R}^n), other generalizations (30C65) Analysis on other specific Lie groups (43A80) Sobolev (and similar kinds of) spaces of functions on metric spaces; analysis on metric spaces (46E36)

Related Items (1)

Continuity of the mappings with finite distortion of the Sobolev class \(W^1_{\nu,\operatorname{loc}}\) on Carnot groups

Cites Work

• A coarea formula for smooth contact mappings of Carnot-Carathéodory spaces
• Hypoelliptic differential operators and nilpotent groups
• Monotone functions and quasiconformal mappings on Carnot groups
• Trace theorems for vector fields
• Sobolev spaces on an arbitrary metric space
• The regularity of inverses to Sobolev mappings and the theory of \(\mathcal{Q}_{q,p} \)-homeomorphisms
• Ahlfors type estimates for perimeter measures in Carnot-Carathéodory spaces
• Space mappings with bounded distortion
• Lipschitz spaces and Calderón-Zygmund operators associated to non-doubling measures
• Stratified Lie Groups and Potential Theory for their Sub-Laplacians
• CAPACITY OF CONDENSERS AND SPATIAL MAPPINGS QUASICONFORMAL IN THE MEAN
• Pointwise Differentiability and Absolute Continuity
• Lusin's condition (N) and mappings of the class W1, n.
• Sobolev met Poincaré
• Differentiability of maps of Carnot groups of Sobolev classes
• Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28
• Non-doubling Ahlfors measures, perimeter measures, and the characterization of the trace spaces of Sobolev functions in Carnot-Carathéodory spaces
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