论文标题
谐波功能的衍生物的精致雷利希边界不等式
Refined Rellich boundary inequalities for the derivatives of a harmonic function
论文作者
论文摘要
经典的Rellich不平等意味着谐波功能的正常和切向衍生物的$ l^2 $ norms等效。在本说明中，我们证明了几种精致的不平等现象，即使域不是Lipschitz，也很有意义。对于二维域，我们通过使用Riemann映射和插值参数获得了$ 1 <p \ leq 2 $的清晰$ l^p $ estimate。
The classical Rellich inequalities imply that the $L^2$-norms of the normal and tangential derivatives of a harmonic function are equivalent. In this note, we prove several refined inequalities, which make sense even if the domain is not Lipschitz. For two-dimensional domains, we obtain a sharp $L^p$-estimate for $1<p\leq 2$ by using a Riemann mapping and interpolation argument.
