On the necessity of the constant rank condition for $L^p$ estimates
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. 88 (1971), no. 1, p. 229-305) shows that if the operator has constant rank then the estimate holds. We prove necessit...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Académie des sciences
2021-01-01
|
| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.105/ |
| _version_ | 1797651517810933760 |
|---|---|
| author | Guerra, André Raiţă, Bogdan |
| author_facet | Guerra, André Raiţă, Bogdan |
| author_sort | Guerra, André |
| collection | DOAJ |
| description | 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. 88 (1971), no. 1, p. 229-305) shows that if the operator has constant rank then the estimate holds. We prove necessity of the constant rank condition for such an estimate. |
| first_indexed | 2024-03-11T16:16:54Z |
| format | Article |
| id | doaj.art-0f3ace5c66ed411bb485be97dd9692f8 |
| institution | Directory Open Access Journal |
| issn | 1778-3569 |
| language | English |
| last_indexed | 2024-03-11T16:16:54Z |
| publishDate | 2021-01-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj.art-0f3ace5c66ed411bb485be97dd9692f82023-10-24T14:18:49ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692021-01-013589-101091109510.5802/crmath.10510.5802/crmath.105On the necessity of the constant rank condition for $L^p$ estimatesGuerra, André0Raiţă, Bogdan1University of Oxford, Andrew Wiles Building, Woodstock Rd, Oxford OX2 6GG, United KingdomMax Planck Institute for Mathematics in the Sciences, Inselstraße 22, 04103 Leipzig, GermanyWe 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. 88 (1971), no. 1, p. 229-305) shows that if the operator has constant rank then the estimate holds. We prove necessity of the constant rank condition for such an estimate.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.105/ |
| spellingShingle | Guerra, André Raiţă, Bogdan On the necessity of the constant rank condition for $L^p$ estimates Comptes Rendus. Mathématique |
| title | On the necessity of the constant rank condition for $L^p$ estimates |
| title_full | On the necessity of the constant rank condition for $L^p$ estimates |
| title_fullStr | On the necessity of the constant rank condition for $L^p$ estimates |
| title_full_unstemmed | On the necessity of the constant rank condition for $L^p$ estimates |
| title_short | On the necessity of the constant rank condition for $L^p$ estimates |
| title_sort | on the necessity of the constant rank condition for l p estimates |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.105/ |
| work_keys_str_mv | AT guerraandre onthenecessityoftheconstantrankconditionforlpestimates AT raitabogdan onthenecessityoftheconstantrankconditionforlpestimates |