On boundary values of three-harmonic Poisson integral on the boundary of a unit disk

• Date: 2018
• Main Authors: Hembars'ka, S. B., Гембарська, С. В
• Format: Article
• Language: Ukrainian
• Published: Institute of Mathematics, NAS of Ukraine 2018
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/1602
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

Let $C_0$ be a curve in a disk $D = \{ | z| < 1\}$ tangential to a circle at the point $z = 1$ and let $C_{\theta}$ be the result of rotation of this curve about the origin $z = 0$ by an angle \theta . We construct a bounded function $u(z)$ three-harmonic in $D$ with zero normal derivatives...