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| Main Author: | |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2207.06073 |
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Table of Contents:
- In this work, a new approach to obtain a solenoidal Lipschitz truncation is presented. More precisely, the goal of the truncation is to modify a function $u \in W^{1,p}(\mathbb{R}^3,\mathbb{R}^3)$ that satisfies the additional constraint $\mathrm{div}~ u=0$, such that its modification $\tilde{u}$ is in $W^{1,\infty}(\mathbb{R}^3,\mathbb{R}^3)$ and still is divergence-free. We give an alternative approach to Lipschitz truncation compared to previous works by Breit, Diening & Fuchs (2012) and Breit, Diening & Schwarzacher (2013). The ansatz pursued here allows a rather strict bound on the $W^{1,p}$ distance of $u$ and $\tilde{u}$.