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Article Dirichlet-Type Problems for n-poisson Equation in Clifford Analysis(Taylor & Francis Ltd, 2022) Aksoy, Umit; Celebi, A. OkayIterated Dirichlet problem, also called as Riquier or Navier problem, and polyharmonic Dirichlet problem are studied for n-Poisson equation in Clifford analysis using iterated polyharmonic Green function and polyharmonic Green-Almansi type function appropriate for the boundary conditions of the problems.Article Citation - WoS: 6Citation - Scopus: 9Dirichlet Problem for a Generalized Inhomogeneous Polyharmonic Equation in an Annular Domain(Taylor & Francis Ltd, 2012) Aksoy, U.; Celebi, A. O.In this article, we investigate the solvability of the Dirichlet problems in ring domains for elliptic linear complex partial differential equations having polyharmonic operators as main parts. First, we give higher order Green functions as fundamental solutions of the homogeneous problems using the iteration of harmonic Green functions for ring domains. Second, we introduce some classes of operators related to Dirichlet problems together with their basic properties. Next, we transform the original problems into equivalent singular integral equations. Finally, solvability of the problems is discussed by defining the adjoint problems and using Fredholm alternative.
