On boundary values of three-harmonic Poisson integral on the boundary of a unit disk
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...
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| Дата: | 2018 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Українська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2018
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/1602 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | 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 $\cfrac{\partial u}{\partial n}$
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 $. |
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