Dirichlet Problems for Harmonic Functions in Half Spaces

  • Lei Qiao


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.
How to Cite
Qiao, L. “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.
Research articles