A remark on the Dirichlet problem in a half-plane

作者:Zhao Tao; Yamada Alexander Jr*
来源:JOURNAL OF INEQUALITIES AND APPLICATIONS, 2014, 2014(1): 497.
DOI:10.1186/1029-242X-2014-497

摘要

In this paper, we prove that if the positive part u(+)(z) of a harmonic function u(z) in a half-plane satisfies a slowly growing condition, then its negative part u(-)(z) can also be dominated by a similarly growing condition. Further, a solution of the Dirichlet problem in a half-plane for a fast growing continuous boundary function is constructed by the generalized Dirichlet integral with this boundary function.