ABSTRACT
One of the most important problems of applied mathematics leads to the extension problem for the solutions of the system of partial differential equations. This chapter focuses on the application of extension theorem of the solution of a first order general linear system of partial differential equations. It presents a study of the problem of the extension of the Riezse system, the Moisil-Theodorescu and the Vinogradov system with additional conditions. The chapter introduces some notations, definitions, and some extension theorems for the general system of partial differential equations. It shows some sufficient conditions for the extension of the above mentioned systems, along with some examples for the application of the theorems.
