Mappings of L p -integrable distortion: regularity of the inverse
Abstract
Let X be an open set in R
n
and suppose that f : X → R
n
is
a Sobolev homeomorphism. We study the regularity of f
−1 under the
L
p
-integrability assumption on the distortion function Kf . First, if X is
the unit ball and p > n−1, then the optimal local modulus of continuity
of f
−1
is attained by a radially symmetric mapping. We show that this
is not the case when p 6 n − 1 and n > 3, and answer a question raised
by S. Hencl and P. Koskela. Second, we obtain the optimal integrability
results for |Df −1
| in terms of the L
p
-integrability assumptions of Kf .
Main Authors
Format
Articles
Research article
Published
2016
Series
Subjects
Publication in research information system
Publisher
The RSE Scotland Foundation
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-201611144618Use this for linking
Review status
Peer reviewed
ISSN
0308-2105
DOI
https://doi.org/10.1017/S0308210515000530
Language
English
Published in
Proceedings of the Royal Society of Edinburgh: Section A Mathematics
Citation
- Onninen, J., & Tengvall, V. (2016). Mappings of L p -integrable distortion: regularity of the inverse. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 146(3), 647-663. https://doi.org/10.1017/S0308210515000530
License
Copyright© Royal Society of Edinburgh 2016. This is a final draft version of an article whose final and definitive form has been published by Royal Society of Edinburgh. Published in this repository with the kind permission of the publisher.