标题： Lipschitz域的光滑逼近、弱曲率和等容量估计 显示英文标题

标题： Smooth approximation of Lipschitz domains, weak curvatures and isocapacitary estimates

摘要： 我们提出了一种新颖的方法，通过一系列光滑的有界域来近似有界Lipschitz域。 我们的方法具有灵活性，可以实现Lipschitz域的内逼近或外逼近，这些域还具有弱定义的曲率，即其边界可以局部描述为属于某个Sobolev空间 $W^{2,q}$ 中某函数图的域 $q\geq 1$。 逼近集的序列也由初始域 $\Omega$ 的一致等容量估计所表征。 显示英文摘要

摘要： We provide a novel approach to approximate bounded Lipschitz domains via a sequence of smooth, bounded domains. The flexibility of our method allows either inner or outer approximations of Lipschitz domains which also possess weakly defined curvatures, namely, domains whose boundary can be locally described as the graph of a function belonging to the Sobolev space $W^{2,q}$ for some $q\geq 1$. The sequences of approximating sets is also characterized by uniform isocapacitary estimates with respect to the initial domain $\Omega$.