Boundary blow up under Sobolev mappings

Abstract

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

11 pages, submitted

Cited by in corpus (1)

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