On the necessity of the constant rank condition for $L^p$ estimates
Classical Analysis and ODEs
2021-02-25 v1 Analysis of PDEs
Abstract
We consider a generalization of the elliptic -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.
Keywords
Cite
@article{arxiv.2007.00484,
title = {On the necessity of the constant rank condition for $L^p$ estimates},
author = {André Guerra and Bogdan Raiţă},
journal= {arXiv preprint arXiv:2007.00484},
year = {2021}
}
Comments
5 pages; weaker versions of the results here had previously appeared in arXiv:1909.03923