Moving gradient singularity for the evolutionary $p$-Laplace equation
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910681356304384 |
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| author | Lindgren, Erik Takahashi, Jin |
| author_facet | Lindgren, Erik Takahashi, Jin |
| contents | We consider the evolutionary $p$-Laplace equation in $\mathbb{R}^n$. For $p>n$, we construct a solution $u$ with a moving gradient singularity in the sense that $|\nabla u(x,t)|\to \infty$ for each $t$ as $x\toξ(t)$, where $ξ:[0,\infty)\to\mathbb{R}^n$ is a given curve. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_00993 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Moving gradient singularity for the evolutionary $p$-Laplace equation Lindgren, Erik Takahashi, Jin Analysis of PDEs We consider the evolutionary $p$-Laplace equation in $\mathbb{R}^n$. For $p>n$, we construct a solution $u$ with a moving gradient singularity in the sense that $|\nabla u(x,t)|\to \infty$ for each $t$ as $x\toξ(t)$, where $ξ:[0,\infty)\to\mathbb{R}^n$ is a given curve. |
| title | Moving gradient singularity for the evolutionary $p$-Laplace equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2411.00993 |