Boundary blow up under Sobolev mappings
Classical Analysis and ODEs
2016-01-20 v1
Abstract
We prove that for mappings continuous up to the boundary, with modulus of continuity satisfying certain divergence condition, the image of the boundary of the unit ball has zero -Hausdorff measure. For H\"older continuous mappings we also prove an essentially sharp generalized Hausdorff dimension estimate.
Cite
@article{arxiv.1304.4295,
title = {Boundary blow up under Sobolev mappings},
author = {Aapo Kauranen and Pekka Koskela},
journal= {arXiv preprint arXiv:1304.4295},
year = {2016}
}
Comments
11 pages, submitted