An alternative approach to solenoidal Lipschitz truncation

Abstract

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 $\tilde{u}$.

24 pages

References in corpus (2)

• A unified theory for some non Newtonian fluids under singular forcing
• Extending Whitney's extension theorem: nonlinear function spaces