2019
Том 71
№ 1

# Dirichlet Problems for Harmonic Functions in Half Spaces

Qiao Lei

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.

English version (Springer): Ukrainian Mathematical Journal 66 (2014), no. 10, pp 1530-1543.

Citation Example: Qiao Lei Dirichlet Problems for Harmonic Functions in Half Spaces // Ukr. Mat. Zh. - 2014. - 66, № 10. - pp. 1367–1378.

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