A Generalized Poincare Inequality for a Class of Constant Coefficient Differential Operators

Abstract

We study first order differential operators with constant coefficients. The main question is under what conditions a generalized Poincaré inequality holds. We show that the constant rank condition is sufficient. The concept of the Moore-Penrose generalized inverse of a matrix comes into play.

7 pages, 0 figures. Major correction of arXiv:0809.1692v2. Submitted to Proceedings of the American Mathematical Society