Using Conservation Laws to Solve Boundary Value Problems for the Moisil–Theodoresco System.

The Moisil–Theodoresco system is a three-dimensional analog of the Cauchy–Riemann system and is related to the spatial static Lamé equations. These equations have been investigated in many papers. Analogs of many results known for the Cauchy–Riemann equations are obtained in these papers. The solutions of the Moisil–Theodoresco system preserve many properties of analytic functions of the complex variable. Some exact solutions of this system are constructed and an infinite series of new conservation laws for the equations of the Moisil–Theodoresco system is given in the present paper. These laws are linear in the derivatives. We use the laws constructed to solve the boundary value problems for the Moisil–Theodoresco system. [ABSTRACT FROM AUTHOR]