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Boundary blow-up under
Sobolev mappings
Aapo Kauranen and Pekka Koskela |
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Vol. 7 (2014), No. 8, 1839–1850
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Abstract |
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We prove that for mappings in , 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 -Hausdorff measure. For Hölder continuous mappings we also prove an essentially sharp generalised Hausdorff dimension estimate. |
Keywords
Sobolev mapping, Hausdorff measure, modulus of continuity
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Mathematical Subject Classification 2010
Primary: 26B10, 26B35, 46E35
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Milestones
Received: 30 July 2013
Revised: 27 August 2014
Accepted: 22 October 2014
Published: 5 February 2015
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Authors |
| Aapo Kauranen | |
| Department of Mathematics and
Statistics University of Jyväskylä P.O. Box 35 (MaD) FI-40014 Jyväskylä Finland |
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| Pekka Koskela | |
| Department of Mathematics and
Statistics University of Jyväskylä P.O. Box 35 (MaD) FI-40014 Jyväskylä Finland |
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