Abdi Tadesse (PhD)Shigute Wodefit2018-07-192023-11-042018-07-192023-11-042014-08http://etd.aau.edu.et/handle/123456789/9363In this project paper we investigated solution for interior Dirichlet problem as main parts. First, we showed uniqueness and continuity of Dirichlet problem in bounded region using maximum and minimum principle. Next, we transform the Laplace equation in two dimensional Cartesian coordinate to Laplace equation in two dimensional polar coordinate. Finally, the Dirichlet problem in bounded domain using separation of variable and Fourier series by appealing to annular region, rectangular region, heat equation and potential theory were discussedenInterior Dirichlet ProblemExistence of ResultsThesis