Syzygies, constant rank, and beyond
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866916080799186944 |
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| author | Härkönen, Marc Nicklasson, Lisa Raiţă, Bogdan |
| author_facet | Härkönen, Marc Nicklasson, Lisa Raiţă, Bogdan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_12663 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Syzygies, constant rank, and beyond Härkönen, Marc Nicklasson, Lisa Raiţă, Bogdan Analysis of PDEs Commutative Algebra 13N10, 13P25, 35G35, 49J45 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. |
| title | Syzygies, constant rank, and beyond |
| topic | Analysis of PDEs Commutative Algebra 13N10, 13P25, 35G35, 49J45 |
| url | https://arxiv.org/abs/2112.12663 |