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Title: Differentiability of maps of Carnot groups of Sobolev classes

Abstract

The P-differentiability in the topology of the Sobolev space of weakly contact maps of Carnot groups is proved. The P-differentiability in the sense of Pansu of contact maps in the class W{sub p}{sup 1}, p>{nu}, and other results are established as consequences. The method of proof is new even in the case of a Euclidean space and yields, for instance, a new proof of well-known results of Reshetnyak and Calderon-Zygmund on the differentiability of functions of Sobolev classes. In addition, a new proof of Lusin's condition N is given for quasimonotone maps in the class W{sub {nu}}{sup 1}. As a consequence, change-of-variables formulae are obtained for maps of Carnot groups.

Authors:
 [1]
  1. S.L. Sobolev Institute for Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk (Russian Federation)
Publication Date:
OSTI Identifier:
21208324
Resource Type:
Journal Article
Journal Name:
Sbornik. Mathematics
Additional Journal Information:
Journal Volume: 194; Journal Issue: 6; Other Information: DOI: 10.1070/SM2003v194n06ABEH000742; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1064-5616
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; EUCLIDEAN SPACE; FUNCTIONS; GROUP THEORY; MAPS; TOPOLOGY

Citation Formats

Vodop'yanov, S K. Differentiability of maps of Carnot groups of Sobolev classes. United States: N. p., 2003. Web. doi:10.1070/SM2003V194N06ABEH000742; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).
Vodop'yanov, S K. Differentiability of maps of Carnot groups of Sobolev classes. United States. doi:10.1070/SM2003V194N06ABEH000742; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).
Vodop'yanov, S K. Mon . "Differentiability of maps of Carnot groups of Sobolev classes". United States. doi:10.1070/SM2003V194N06ABEH000742; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).
@article{osti_21208324,
title = {Differentiability of maps of Carnot groups of Sobolev classes},
author = {Vodop'yanov, S K},
abstractNote = {The P-differentiability in the topology of the Sobolev space of weakly contact maps of Carnot groups is proved. The P-differentiability in the sense of Pansu of contact maps in the class W{sub p}{sup 1}, p>{nu}, and other results are established as consequences. The method of proof is new even in the case of a Euclidean space and yields, for instance, a new proof of well-known results of Reshetnyak and Calderon-Zygmund on the differentiability of functions of Sobolev classes. In addition, a new proof of Lusin's condition N is given for quasimonotone maps in the class W{sub {nu}}{sup 1}. As a consequence, change-of-variables formulae are obtained for maps of Carnot groups.},
doi = {10.1070/SM2003V194N06ABEH000742; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)},
journal = {Sbornik. Mathematics},
issn = {1064-5616},
number = 6,
volume = 194,
place = {United States},
year = {2003},
month = {6}
}