论文标题
通用Stokes运算符的非本地方法，具有有界的可测量系数
A non-local approach to the generalized Stokes operator with bounded measurable coefficients
论文作者
论文摘要
我们在$ l^p_σ（\ Mathbb {r}^d）$，$ d \ geq 2 $上建立了具有有界可测量系数的Stokes运算符的功能分析性能，对于$ \ lvert 1 / p -1 / p -1 /2 \ rvert <1 / d $。其中包括最佳分解界和最大$ l^q $ regularity的属性。我们进一步对解决方案的梯度进行了规律性估计，以通过有限的可测量系数分解问题。作为这些结果的关键，我们确定了非本地caccioppoli不平等的有效性，对解决方案解决方案的解决方案。
We establish functional analytic properties of the Stokes operator with bounded measurable coefficients on $L^p_σ (\mathbb{R}^d)$, $d \geq 2$, for $\lvert 1 / p - 1 / 2 \rvert < 1 / d$. These include optimal resolvent bounds and the property of maximal $L^q$-regularity. We further give regularity estimates on the gradient of the solution to the Stokes resolvent problem with bounded measurable coefficients. As a key to these results we establish the validity of a non-local Caccioppoli inequality to solutions of the Stokes resolvent problem.
