Comptes Rendus. Mathématique (Jan 2021)
On the necessity of the constant rank condition for $L^p$ estimates
Abstract
We consider a generalization of the elliptic $L^p$-estimate suited for linear operators with non-trivial kernels. A classical result of Schulenberger and Wilcox (Ann. Mat. Pura Appl. 88 (1971), no. 1, p. 229-305) shows that if the operator has constant rank then the estimate holds. We prove necessity of the constant rank condition for such an estimate.