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2014 Boundary blow-up under Sobolev mappings
Aapo Kauranen, Pekka Koskela
Anal. PDE 7(8): 1839-1850 (2014). DOI: 10.2140/apde.2014.7.1839

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.

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Aapo Kauranen. Pekka Koskela. "Boundary blow-up under Sobolev mappings." Anal. PDE 7 (8) 1839 - 1850, 2014. https://doi.org/10.2140/apde.2014.7.1839

Information

Received: 30 July 2013; Revised: 27 August 2014; Accepted: 22 October 2014; Published: 2014
First available in Project Euclid: 20 December 2017

zbMATH: 1312.26024
MathSciNet: MR3318741
Digital Object Identifier: 10.2140/apde.2014.7.1839

Subjects:
Primary: 26B10 , 26B35 , 46E35

Keywords: Hausdorff measure , modulus of continuity , Sobolev mapping

Rights: Copyright © 2014 Mathematical Sciences Publishers

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