Analysis & PDE
- Anal. PDE
- Volume 7, Number 8 (2014), 1839-1850.
Boundary blow-up under Sobolev mappings
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.
Anal. PDE, Volume 7, Number 8 (2014), 1839-1850.
Received: 30 July 2013
Revised: 27 August 2014
Accepted: 22 October 2014
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 26B10: Implicit function theorems, Jacobians, transformations with several variables 26B35: Special properties of functions of several variables, Hölder conditions, etc. 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems
Kauranen, Aapo; Koskela, Pekka. Boundary blow-up under Sobolev mappings. Anal. PDE 7 (2014), no. 8, 1839--1850. doi:10.2140/apde.2014.7.1839. https://projecteuclid.org/euclid.apde/1513731626