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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.05204 |
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| _version_ | 1866916386215821312 |
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| author | Ignat, Radu |
| author_facet | Ignat, Radu |
| contents | We give a short and self-contained proof of the interior $\mathcal C^{1,1}$ regularity of solutions $φ:Ω\to \mathbb{R}$ to the eikonal equation $|\nabla φ|=1$ in an open set $Ω\subset \mathbb{R}^{N}$ in dimension $N\geq 1$ under the assumption that $φ$ is pointwise differentiable in $Ω$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_05204 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A short proof of the $\mathcal C^{1,1}$ regularity for the eikonal equation Ignat, Radu Analysis of PDEs We give a short and self-contained proof of the interior $\mathcal C^{1,1}$ regularity of solutions $φ:Ω\to \mathbb{R}$ to the eikonal equation $|\nabla φ|=1$ in an open set $Ω\subset \mathbb{R}^{N}$ in dimension $N\geq 1$ under the assumption that $φ$ is pointwise differentiable in $Ω$. |
| title | A short proof of the $\mathcal C^{1,1}$ regularity for the eikonal equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2409.05204 |