Obstacles for Sobolev-homeomorphisms with low rank -- pointwise a.e. vs distributional Jacobians
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916313345032192 |
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| author | Park, Woongbae Schikorra, Armin |
| author_facet | Park, Woongbae Schikorra, Armin |
| contents | We show that for any $k$ and $s > \frac{k+1}{k+2}$ there exist neither $W^{s,\frac{k}{s}}$-Sobolev nor $C^s$-Hölder 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_03853 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Obstacles for Sobolev-homeomorphisms with low rank -- pointwise a.e. vs distributional Jacobians Park, Woongbae Schikorra, Armin Analysis of PDEs Algebraic Geometry We show that for any $k$ and $s > \frac{k+1}{k+2}$ there exist neither $W^{s,\frac{k}{s}}$-Sobolev nor $C^s$-Hölder 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. |
| title | Obstacles for Sobolev-homeomorphisms with low rank -- pointwise a.e. vs distributional Jacobians |
| topic | Analysis of PDEs Algebraic Geometry |
| url | https://arxiv.org/abs/2407.03853 |