Differentiability of maps of Carnot groups of Sobolev classes

DOI10.1070/SM2003v194n06ABEH000742zbMath1078.46026OpenAlexW1978067107MaRDI QIDQ4658210

S. K. Vodo'Yanov

Publication date: 16 March 2005

Published in: Sbornik: Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1070/sm2003v194n06abeh000742

zbMATH Keywords

Sobolev spacedifferentiabilityCarnot groupchange-of-variables formulae

Mathematics Subject Classification ID

Quasiconformal mappings in (mathbb{R}^n), other generalizations (30C65) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35)

Related Items (16)

Functional and analytical properties of a class of mappings of quasiconformal analysis on Carnot groups ⋮ On value distributions for quasimeromorphic mappings on \(\mathbb H\)-type Carnot groups ⋮ Continuity of the mappings with finite distortion of the Sobolev class \(W^1_{\nu,\operatorname{loc}}\) on Carnot groups ⋮ Capacity estimates, Liouville's theorem, and singularity removal for mappings with bounded \((p,q)\)-distortion ⋮ Hölder continuity of the traces of Sobolev functions to hypersurfaces in Carnot groups and the \(\mathcal{P} \)-differentiability of Sobolev mappings ⋮ Openness and discreteness of mappings of finite distortion on Carnot groups ⋮ Two-weighted composition operators on Sobolev spaces and quasiconformal analysis ⋮ Topological properties of mappings with finite distortion on Carnot groups ⋮ Mappings with bounded \((P,Q)\)-distortion on Carnot groups ⋮ On the regularity of the Poletskii function under weak analytic assumptions on the given mapping ⋮ The regularity of inverses to Sobolev mappings and the theory of \(\mathcal{Q}_{q,p} \)-homeomorphisms ⋮ Admissible changes of variables for Sobolev functions on (sub-)Riemannian manifolds ⋮ Isomorphisms of Sobolev spaces on Carnot groups and quasi-isometric mappings ⋮ Basics of the quasiconformal analysis of a two-index scale of spatial mappings ⋮ Isomorphisms of Sobolev spaces on Riemannian manifolds and quasiconformal mappings ⋮ Isomorphisms of Sobolev spaces on Carnot groups and quasiconformal mappings

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