An alternative approach to solenoidal Lipschitz truncation
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866914252299698176 |
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| author | Schiffer, Stefan |
| author_facet | Schiffer, Stefan |
| 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 $\tilde{u}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_06073 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | An alternative approach to solenoidal Lipschitz truncation Schiffer, Stefan Analysis of PDEs 26B20, 26B35 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 $\tilde{u}$. |
| title | An alternative approach to solenoidal Lipschitz truncation |
| topic | Analysis of PDEs 26B20, 26B35 |
| url | https://arxiv.org/abs/2207.06073 |