Differentiability of maps of Carnot groups of Sobolev classes
Sbornik. Mathematics, Tome 194 (2003) no. 6, pp. 857-877
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The $\mathscr P$-differentiability in the topology of the Sobolev space of weakly contact maps of Carnot groups is proved.
The $\mathscr P$-differentiability in the sense of Pansu of contact maps in
the class $W_p^1$, $p>\nu$, 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 $\mathscr N$ is given for quasimonotone maps in the class $W_\nu^1$. As a consequence, change-of-variables formulae are obtained for maps of Carnot groups.
@article{SM_2003_194_6_a3,
author = {S. K. Vodop'yanov},
title = {Differentiability of maps of {Carnot} groups of {Sobolev} classes},
journal = {Sbornik. Mathematics},
pages = {857--877},
publisher = {mathdoc},
volume = {194},
number = {6},
year = {2003},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2003_194_6_a3/}
}
S. K. Vodop'yanov. Differentiability of maps of Carnot groups of Sobolev classes. Sbornik. Mathematics, Tome 194 (2003) no. 6, pp. 857-877. http://geodesic.mathdoc.fr/item/SM_2003_194_6_a3/