Ciarlet Nečas condition in fractional Sobolev spaces
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| Format: | Preprint |
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2026
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| _version_ | 1866910072188174336 |
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| author | Hencl, Stanislav Mielec, Jaromír Mohanta, Kaushik |
| author_facet | Hencl, Stanislav Mielec, Jaromír Mohanta, Kaushik |
| contents | Let $s\in(\frac{n}{n+1},1)$, $Ω\subset\mathbb{R}^n$ be an open set and let $f\in W^{s,n/s}(Ω,\mathbb{R}^n)$ be mapping with positive distributional Jacobian $\mathcal{J}_f>0$ which models some deformation in fractional Nonlinear Elasticity. We show change of variables formula in this class and as a consequence we show that the analogue of Ciarlet-Nečas condition $\mathcal{J}_f(Ω)=|f(Ω)|$ implies that our mapping is one-to-one a.e. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_24234 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Ciarlet Nečas condition in fractional Sobolev spaces Hencl, Stanislav Mielec, Jaromír Mohanta, Kaushik Functional Analysis Analysis of PDEs Let $s\in(\frac{n}{n+1},1)$, $Ω\subset\mathbb{R}^n$ be an open set and let $f\in W^{s,n/s}(Ω,\mathbb{R}^n)$ be mapping with positive distributional Jacobian $\mathcal{J}_f>0$ which models some deformation in fractional Nonlinear Elasticity. We show change of variables formula in this class and as a consequence we show that the analogue of Ciarlet-Nečas condition $\mathcal{J}_f(Ω)=|f(Ω)|$ implies that our mapping is one-to-one a.e. |
| title | Ciarlet Nečas condition in fractional Sobolev spaces |
| topic | Functional Analysis Analysis of PDEs |
| url | https://arxiv.org/abs/2603.24234 |