English

Boundary blow up under Sobolev mappings

Classical Analysis and ODEs 2016-01-20 v1

Abstract

We prove that for mappings W1,n(Bn,Rn),W^{1,n}(B^n, \R^n), continuous up to the boundary, with modulus of continuity satisfying certain divergence condition, the image of the boundary of the unit ball has zero nn-Hausdorff measure. For H\"older continuous mappings we also prove an essentially sharp generalized Hausdorff dimension estimate.

Keywords

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

R2 v1 2026-06-22T00:00:11.705Z