Journal
JOURNAL OF SYMBOLIC COMPUTATION
Volume 123, Issue -, Pages -Publisher
ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jsc.2023.102274
Keywords
Linear PDE; Constant rank operator; Controllable operator; Primary decomposition of modules; Syzygies
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We study linear PDE with constant coefficients and investigate the connection between the constant rank condition and primary decomposition. We also make 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.
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. (c) 2023 Published by Elsevier Ltd.
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