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. (4) 88: 229-305, 1971) shows that if the operator has constant rank then the estimate holds. We prove necessity of the constant rank condition for such an estimate.
Highlights
If and only if A is elliptic; this is a classical result that goes back to the work of Calderón– Zygmund [3]
We consider a generalization of the elliptic Lp -estimate suited for linear operators with non-trivial kernels
We prove necessity of the constant rank condition for such an estimate. 2020 Mathematics Subject Classification. 26D10, 42B20
Summary
If and only if A is elliptic; this is a classical result that goes back to the work of Calderón– Zygmund [3]. We consider a generalization of the elliptic Lp -estimate suited for linear operators with non-trivial kernels. 229-305) shows that if the operator has constant rank the estimate holds.
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