On the Neumann problem for harmonic functions in the upper half plane

• DOI: 10.1016/j.jmaa.2014.04.076
• Publication Date: 2014-05-09T08:41:49Z
• Authors: Kaizheng Wang
• Keywords: Harmonic measure; Harmonic; Neumann series; Constant (computer programming)

Abstract This paper is devoted to bounded harmonic functions in the upper half plane R + 2 with two types of prescribed Neumann boundary data: continuous with compact support and periodic. By developing an explicit formula and harmonic extensions we present the sufficient and necessary condition for the existence of bounded harmonic functions for the boundary value problems. The uniqueness up to an arbitrary constant and periodicity are also proved.