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arXiv · 2407.03853

Obstacles for Sobolev-homeomorphisms with low rank -- pointwise a.e. vs distributional Jacobians

Woongbae Park·Armin Schikorra
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Abstract

We show that for any $k$ and $s > \frac{k+1}{k+2}$ there exist neither $W^{s,\frac{k}{s}}$-Sobolev nor $C^s$-H\"older homeomorphisms from the disk $\mathbb{B}^n$ into $\mathbb{R}^N$ whose gradient has rank $< k$ in distributional sense. This complements known examples of such kind of homeomorphisms whose gradient has rank $<k$ almost everywhere.

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Woongbae Park, Armin Schikorra. 2024-07-04. Obstacles for Sobolev-homeomorphisms with low rank -- pointwise a.e. vs distributional Jacobians. https://arxiv.org/abs/2407.03853

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