Levi functions for linear elliptic systems with variable coefficients including shell equations

Abstract

This paper gives an algorithm to construct Levi functions of arbitrary degree for elliptic systems of linear partial differential equations with variable (real-analytic) coefficients. Further, an indirect method is described to transform elliptic boundary value problems into a system of integral equations. This method is applied to the shell equations in the non-shallow case. (In the shallow case the shell equations have constant coefficients.) Some questions of discretization are discussed and numerical results are presented.