2019
Том 71
№ 8

Qiao Lei

Articles: 1
Article (Ukrainian)

Dirichlet Problems for Harmonic Functions in Half Spaces

Ukr. Mat. Zh. - 2014. - 66, № 10. - pp. 1367–1378

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.