$W^{s,\frac{n}{s}}$-maps with positive distributional Jacobians
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2019
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| _version_ | 1866911459915595776 |
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| author | Li, Siran Schikorra, Armin |
| author_facet | Li, Siran Schikorra, Armin |
| contents | We extend the well-known result that any $f \in W^{1,n}(Ω,\mathbb{R}^n)$, $Ω\subset \mathbb{R}^n$ with strictly positive Jacobian is actually continuous: it is also true for fractional Sobolev spaces $W^{s,\frac{n}{s}}(Ω)$ for any $s \geq \frac{n}{n+1}$, where the sign condition on the Jacobian is understood in a distributional sense.
Along the way we also obtain extensions to fractional Sobolev spaces $W^{s,\frac{n}{s}}$ of the degree estimates known for $W^{1,n}$-maps with positive or non-negative Jacobian, such as the sense-preserving property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1905_07338 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | $W^{s,\frac{n}{s}}$-maps with positive distributional Jacobians Li, Siran Schikorra, Armin Analysis of PDEs Differential Geometry Functional Analysis We extend the well-known result that any $f \in W^{1,n}(Ω,\mathbb{R}^n)$, $Ω\subset \mathbb{R}^n$ with strictly positive Jacobian is actually continuous: it is also true for fractional Sobolev spaces $W^{s,\frac{n}{s}}(Ω)$ for any $s \geq \frac{n}{n+1}$, where the sign condition on the Jacobian is understood in a distributional sense. Along the way we also obtain extensions to fractional Sobolev spaces $W^{s,\frac{n}{s}}$ of the degree estimates known for $W^{1,n}$-maps with positive or non-negative Jacobian, such as the sense-preserving property. |
| title | $W^{s,\frac{n}{s}}$-maps with positive distributional Jacobians |
| topic | Analysis of PDEs Differential Geometry Functional Analysis |
| url | https://arxiv.org/abs/1905.07338 |