Some Riemann Boundary Value Problems In Complex Clifford Analysis And Several Complex Variables And Carleman Boundary Value Problems For The Modified Helmholtz Equations In R~2

In this thesis, we investigate some Riemann boundary value problems in complex Clifford analysis and several complex variables, then give the solvable conditions of these problems and the integral expressions of the solutions. we also investigate the Carleman boundary value problems with the boundary condition w+[β(t)]=G(t)w+(t)+g(t), t∈Γ for the modified Helmholtz equation of first order on multiply connected domains of R2. By using the methods from generalized analytic functions, we obtain the existence of solutions and the solvable conditions for the above problem respectively in different cases.