Abdi Tadesse (PhD)Kumelachew Bizuayehu2020-12-172023-11-042020-12-172023-11-042016-09-09http://etd.aau.edu.et/handle/123456789/24155In this paper, we shall study linear elliptic partial differential equations of second order, ( ) ( ) ( ) 0 ,     i j i ij ij i i Lu a x u b x u c x u on a bounded domain n   R with regular boundary . The coefficients aij , bi and c are assumed to be continuous. We will see that if u is a solution of the PDE then it attains its maximum/minimum on.enMaximum PrincipleElliptic PdesLaplace EquationDirichlet ProblemHarmonic FunctionExistence and UniquenessA Prior BoundsThesis