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arXiv · 1007.2091

Generalized Hausdorff dimension distortion in Euclidean spaces under Sobolev mappings

Tapio Rajala·Aleksandra Zapadinskaya·Thomas Zürcher
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Abstract

We investigate how the integrability of the derivatives of Orlicz-Sobolev mappings defined on open subsets of $\mathbb{R}^n$ affect the sizes of the images of sets of Hausdorff dimension less than $n$. We measure the sizes of the image sets in terms of generalized Hausdorff measures.

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Tapio Rajala, Aleksandra Zapadinskaya, Thomas Zürcher. 2010-07-13. Generalized Hausdorff dimension distortion in Euclidean spaces under Sobolev mappings. https://arxiv.org/abs/1007.2091

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