Dirichlet Problems for Harmonic Functions in Half Spaces

• Date: 2014
• Main Authors: Qiao, Lei, Кіао, Лей
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2014
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2228
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

In our paper, we prove that if the positive part $u^{+}(x)$ of a harmonic function $u(x)$ in a half space satisfies the condition of slow growth, then its negative part $u^{-}(x)$ can also be dominated by a similar growth condition. Moreover, we give an integral representation of the function $u(x)$...