TY - JOUR
AU - S. B. Hembars'ka
PY - 2018/07/25
Y2 - 2020/12/05
TI - On boundary values of three-harmonic Poisson integral on the boundary
of a unit disk
JF - Ukrainsâ€™kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 70
IS - 7
SE - Research articles
DO -
UR - http://umj.imath.kiev.ua/index.php/umj/article/view/1602
AB - 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 rotationof this curve about the origin $z = 0$ by an angle \theta . We construct a bounded function $u(z)$ three-harmonic in $D$ with zeronormal derivatives $\cfrac{\partial u}{\partial n}$and $\cfrac{\partial 2u}{\partial r_2}$on the boundary such that the limit along $C_{\theta}$ does not exist for all $\theta , 0 \leq \theta \leq 2\pi $.
ER -