Regularity of mappings inverse to Sobolev mappings
Sbornik. Mathematics, Tome 203 (2012) no. 10, pp. 1383-1410
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For homeomorphisms $\varphi\colon\Omega\to \Omega'$ on Euclidean domains in $\mathbb R^n$, $n\geqslant2$, necessary and sufficient conditions ensuring that the inverse mapping belongs to a Sobolev class are investigated. The result obtained is used to describe a new two-index scale of homeomorphisms in some Sobolev class such that their inverses also form a two-index scale of mappings, in another Sobolev class.
This scale involves quasiconformal mappings and also homeomorphisms in the Sobolev class $W^1_{n-1}$ such that $\operatorname{rank}D\varphi(x)\leqslant n-2$ almost everywhere on the zero set of the Jacobian
$\det D\varphi(x)$.
Bibliography: 65 titles.
Keywords:
Sobolev class of mappings, approximate differentiability, distortion and codistortion of mappings, generalized quasiconformal mapping, composition operator.
@article{SM_2012_203_10_a0,
author = {S. K. Vodopyanov},
title = {Regularity of mappings inverse to {Sobolev} mappings},
journal = {Sbornik. Mathematics},
pages = {1383--1410},
publisher = {mathdoc},
volume = {203},
number = {10},
year = {2012},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2012_203_10_a0/}
}
S. K. Vodopyanov. Regularity of mappings inverse to Sobolev mappings. Sbornik. Mathematics, Tome 203 (2012) no. 10, pp. 1383-1410. http://geodesic.mathdoc.fr/item/SM_2012_203_10_a0/