Vol. 7, No. 8, 2014

Download this article
Download this article For screen
For printing
Recent Issues

Volume 16
Issue 2, 309–612
Issue 1, 1–308

Volume 15, 8 issues

Volume 14, 8 issues

Volume 13, 8 issues

Volume 12, 8 issues

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Author Index
To Appear
 
Other MSP Journals
Boundary blow-up under Sobolev mappings

Aapo Kauranen and Pekka Koskela

Vol. 7 (2014), No. 8, 1839–1850
Abstract

We prove that for mappings in W1,n(n, m), continuous up to the boundary and with modulus of continuity satisfying a certain divergence condition, the image of the boundary of the unit ball has zero n-Hausdorff measure. For Hölder continuous mappings we also prove an essentially sharp generalised Hausdorff dimension estimate.

Keywords
Sobolev mapping, Hausdorff measure, modulus of continuity
Mathematical Subject Classification 2010
Primary: 26B10, 26B35, 46E35
Milestones
Received: 30 July 2013
Revised: 27 August 2014
Accepted: 22 October 2014
Published: 5 February 2015
Authors
Aapo Kauranen
Department of Mathematics and Statistics
University of Jyväskylä
P.O. Box 35 (MaD)
FI-40014 Jyväskylä
Finland
Pekka Koskela
Department of Mathematics and Statistics
University of Jyväskylä
P.O. Box 35 (MaD)
FI-40014 Jyväskylä
Finland