The Green Matrix for Strongly Elliptic Systems of Second Order with Continuous Coefficients

Abstract

We study a generalization of the Green function for elliptic equations to elliptic systems of second order with continuous coefficients. The existence and uniqueness of such a Green matrix as well as various estimates concerning the growth properties near the singular diagonal are proved. Moreover, one can derive representation formulas for solutions of elliptic systems and deduce from these further information about the solution even in the case when the right-hand side of the system is a vector-valued measure of bounded variation.