ON THE SCHWARZ PROBLEM FOR THE MOISIL–TEODORESCU SYSTEM IN A SPHERICAL LAYER AND IN THE INTERIOR OF A TORUS

Abstract

Doubly connected regions play a significant role in fluid mechanics. For example, the flow created by a long solid cylinder moving in the direction of the normal to its axis occurs precisely in a doubly connected region.In this paper, well-posed problems for the Moisil--Teodorescu system are presented in the case of a spherical layer and the interior of a torus. The Moisil--Teodorescu elliptic system is an example of a multidimensional generalized Cauchy--Riemann system. The results of this work show a significant difference between the well-posed problem in a spherical layer and a similar problem in a torus.

Keywords

• cauchy–riemann system
• moisil–teodorescu system
• schwartz problem
• spherical layer
• torus interior
• solvability of the problem