Dirichlet Problems for Harmonic Functions in Half Spaces

  • Lei Qiao

Abstract

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 $u(x)$. Further, a solution of the Dirichlet problem in the half space for a rapidly growing continuous boundary function is constructed by using the generalized Poisson integral with this boundary function.
Published
25.10.2014
How to Cite
QiaoL. “Dirichlet Problems for Harmonic Functions in Half Spaces”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, no. 10, Oct. 2014, pp. 1367–1378, http://umj.imath.kiev.ua/index.php/umj/article/view/2228.
Section
Research articles