G.Tsegaye (PhD)Aschale Shitaye2018-07-182023-11-042018-07-182023-11-042017-06http://etd.aau.edu.et/handle/123456789/9107Using an appropriate parametrix (Levi function), Dirichlet boundary value problem is reduced to some direct segregated systems of Boundary- Domain Integral Equations (BDIEs). Although the theory of BDIEs in 3D is well developed, the BDIEs in 2D need a special consideration due to their different equivalence properties. Consequently, we need to set conditions on the domain or the spaces to insure the invertibility of corresponding parametrix-based integral layer potentials and hence the unique solubility of BDIEs. The properties of corresponding potential operators are investigated. The equivalence of the original BVP and the obtained BDIEs are analysed and the invertibility of the BDIE operators is proved.enAnalysis of Boundary-Domain IntegralEquations for Variable CoefficientThesis