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arXiv · 2411.00993

Moving gradient singularity for the evolutionary $p$-Laplace equation

Erik Lindgren·Jin Takahashi
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Abstract

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 $x\to\xi(t)$, where $\xi:[0,\infty)\to\mathbb{R}^n$ is a given curve.

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Erik Lindgren, Jin Takahashi. 2024-11-01. Moving gradient singularity for the evolutionary $p$-Laplace equation. https://arxiv.org/abs/2411.00993

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