Abreu Blaya, RicardoBory Reyes, JuanGuzman Adan, AliSchneider, Baruch2023-06-162023-06-1620120096-30031873-5649https://doi.org/10.1016/j.amc.2012.10.022https://hdl.handle.net/20.500.14365/1053In this paper, we study a class of boundary value problems for a first order linear partial differential equation (all of whose solutions are harmonic functions), which is called the Cimmino system. With the help of the one-to-one correspondence between the theory of quaternion valued hyperholomorphic functions and that of Cimmino system's solutions, necessary and sufficient conditions for the solvability of the non-homogeneous Cimmino system coupled by the boundary conditions are derived and its general solution is explicitly described. (C) 2012 Elsevier Inc. All rights reserved.eninfo:eu-repo/semantics/closedAccessCimmino systemQuaternionic analysisBoundary value problemsArticle10.1016/j.amc.2012.10.0222-s2.0-84870055319