论文标题
螺线管Lipschitz截断的另一种方法
An alternative approach to solenoidal Lipschitz truncation
论文作者
论文摘要
在这项工作中，提出了一种新的方法来获得螺线管Lipschitz截断。更准确地说，截断的目的是修改W^{1，p}中的功能$ u \（\ Mathbb {r}^3，\ Mathbb {r}^3）$满足其他约束$ \ mathrm {div} 〜u = 0 $的其他约束$ \ tildefifical $ \ tilde $ \ tilde $} $ $ w^{1，\ infty}（\ mathbb {r}^3，\ mathbb {r}^3）$，并且仍然不含散布。与Breit，Diening＆Fuchs（2012）和Breit，Diening＆Schwarzacher（2013）相比，我们为Lipschitz截断提供了另一种方法。这里追求的Ansatz允许在$ w^{1，p} $ $ u $和$ \ tilde {u} $上受到相当严格的约束。
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 $\tilde{u}$.
