论文标题
维度范围较低的域中的规律性问题
The Regularity problem in domains with lower dimensional boundaries
论文作者
论文摘要
在本文中，我们在域（平坦和Lipschitz）较低尺寸边界的域中规定了规则性边界值问题的可溶性，其系数表现出类似于Dahlberg-Kenig-pipher条件的操作员。 证明遵循的经典策略是在平方函数和非区域最大函数上显示界限。这种设置的主要新颖性和困难是存在多种非界限衍生物。为了解决它，我们考虑了衍生物的圆柱系统，并在“角衍生物”上建立了新的估计。
In the present paper we establish the solvability of the Regularity boundary value problem in domains with (flat and Lipschitz) lower dimensional boundaries for operators whose coefficients exhibit small oscillations analogous to the Dahlberg-Kenig-Pipher condition. The proof follows the classical strategy of showing bounds on the square function and the non-tangential maximal function. The key novelty and difficulty of this setting is the presence of multiple non-tangential derivatives. To solve it, we consider a cylindrical system of derivatives and establish new estimates on the "angular derivatives".
