Gedif, Tsegaye (PhD)Fekade, Behailu2019-11-052023-11-042019-11-052023-11-042016-08-04http://etd.aau.edu.et/handle/123456789/19798Using an appropriate fundamental solution, Dirichlet boundary value problem is reduced to some direct Boundary Integral Equations (BIEs). Although the theory of BIEs in 3D is well developed, the BIEs in 2D need a special consideration due to their di_erent equivalence properties. Consequently, we need to set conditions on the domain for the invertibility of corresponding fundamental based integral layer potentials and hence the unique solvability of BIEs. The properties of corresponding potential operators are investigated. The equivalence of the original BVP and the obtained BIEs are analyzed and the invertibility of the BIE operators is proved.enAnalysis of BoundaryIntegral EquationsLaplace Dirichlet Bvp In 2dThesis