Dirichlet Problems for Harmonic Functions in Half Spaces

• Datum: 2014
• Hauptverfasser: Qiao, Lei, Кіао, Лей
• Format: Artikel
• Sprache: Ukrainisch; Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2014
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/2228
• Назва журналу: 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 $u(x)$...