Abdi Tadesse (PhD)Kassa Gebre2020-12-092023-11-042020-12-092023-11-042014-06-06http://etd.aau.edu.et/handle/123456789/23917In this project we present basic properties of Laplace’s equation on the boundary value problems with the tight focus on mean value property. It is shown that for the Neumann problem, Δ = 0 on Ω × (0 , ∞) = ( ) The boundary data can’t be prescribed at will. Indeed, it is required to satisfy the compatibility condition, ( ) = 0 Regular conditions on the solution u of Δ = 0 are also shown.enLaplace EquationBoundaryValueProblemsThesis