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Boundary value problems for the Cimmino system via quaternionic analysis. (English) Zbl 1311.30030
Summary: In 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.

30G35 Functions of hypercomplex variables and generalized variables
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