Analysis of PDEs, Classical Analysis and ODEs
We study first order differential operators with constant coefficients. The main question is under what conditions a generalized Poincar\'e 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.
Gustafson, Derek, "Elliptic Complexes and Generalized Poincaré Inequalities" (2008). Mathematics Faculty Scholarship. Paper 2.
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