Syzygies, constant rank, and beyond
Abstract
We study linear PDE with constant coefficients. The constant rank condition on a system of linear PDEs with constant coefficients is often used in the theory of compensated compactness. While this is a purely linear algebraic condition, the nonlinear algebra concept of primary decomposition is another important tool for studying such system of PDEs. In this paper we investigate the connection between these two concepts. From the nonlinear analysis point of view, we make some progress in the study of weak lower semicontinuity of integral functionals defined on sequences of PDE constrained fields, when the PDEs do not have constant rank.
 Publication:

arXiv eprints
 Pub Date:
 December 2021
 DOI:
 10.48550/arXiv.2112.12663
 arXiv:
 arXiv:2112.12663
 Bibcode:
 2021arXiv211212663H
 Keywords:

 Mathematics  Analysis of PDEs;
 Mathematics  Commutative Algebra;
 13N10;
 13P25;
 35G35;
 49J45
 EPrint:
 21 pages