On the Moisil-Theodoresco Operator in Orthogonal Curvilinear Coordinates - Bory Reyes, J.; Pérez-de la Rosa, M. A. (Computational methods and function theory, 2021)
The action of the Moisil-Theodoresco operator over a quaternionic valued function defined on R 3 (sum of a scalar and a vector field) in Cartesian coordinates is generally well understood. However this is not the case for any orthogonal curvilinear coordinate system. This paper sheds some new light on the technical aspect of the subject. Moreover, we introduce a notion of quaternionic Laplace operator acting on a quaternionic valued function from which one can recover both scalar and vector Laplacians in the vector analysis context.