An exact transformation of exteriors of ellipsoids onto semi-infinite perpendicular parallelepipeds (Q1209513)

This is a special application of a method of transforming exteriors of a class of three-dimensional bodies onto canonical domains, due to the second author. In the recent case all formulae describing consecutive transformations are exact. The basic idea is: the intersection of the ellipsoids under consideration by a set of planes all containing the \(x\)- axis (of a Cartesian system) are ellipses. Hence, the mapping function for the transformation of the ellipsoid onto a parallelepiped is constructed by the well known conformal mappings of ellipses onto certain canonical domains (e.g. onto circles by means of the Joukowski function), now depending on a (third) parametric variable, which describes the intersecting plane. All transformations have been developed for applications to problems of fluid mechanics -- the authors are well known from their work on hard analysis in the calculation of (plane) Stokes flow cf. [Bull. Acad Pol. Sci., Sér. Sci. Tech. 30, 579-589 (1982; Zbl 0563.76038), ibid. 34, 505-518 (1986; Zbl 0625.76039), and the second author, Acta Mech. 89, No. 1-4, 147-165 (1991; Zbl 0753.76144)], therefore the transformation of first order derivatives and of the Laplacian under the mapping constructed here is added (in explicit form, too).