

Preprint 45/2003
Mappings of finite distortion:The degree of regularity.
Daniel Faraco, Pekka Koskela, and Xiao Zhong
Contact the author: Please use for correspondence this email.
Submission date: 07. May. 2003
Pages: 21
published in: Advances in mathematics, 190 (2005) 2, p. 300-318
DOI number (of the published article): 10.1016/j.aim.2003.12.009
Bibtex
MSC-Numbers: 30C65, 26B10, 73C50
Download full preprint: PDF (209 kB), PS ziped (188 kB)
Abstract:
Recently, a rich theory of mappings of finite distortion has been established.
It has been proved that under natural assumptions on the distortion these mappings
share with the familiar mappings of bounded distortion interesting topological and
and analytical properties. In this paper we concentrate in the self-improving
integrability of these mappings since the existing methods have only yield partial
results (see the Monograph of Iwaniec and Martin for a detailed account about
what was known about these mappings).
We prove the following theorem: Let K(x) be such that
,
.
Then there exists two universal constants
with the following property. Let f be
in
with
and the Jacobian determinant J(x,f) in
. Then
automatically J(x,f) is in
.
As a consequence we obtained novel results on the size of removable sets for bounded functions of finite distortion and on the area distortion under these type of mappings.