On the necessity of the constant rank condition for $L^p$ estimates

André Guerra; Bogdan Raiţă

doi:10.5802/crmath.105

Théorie spectrale, Théorie des opérateurs

On the necessity of the constant rank condition for

L^{p}

estimates

André Guerra ¹ ; Bogdan Raiţă ²

¹ University of Oxford, Andrew Wiles Building, Woodstock Rd, Oxford OX2 6GG, United Kingdom
² Max Planck Institute for Mathematics in the Sciences, Inselstraße 22, 04103 Leipzig, Germany

Comptes Rendus. Mathématique, Volume 358 (2020) no. 9-10, pp. 1091-1095.

Résumé

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.

Reçu le : 2020-07-05
Accepté le : 2020-08-10
Publié le : 2021-01-05

DOI : 10.5802/crmath.105

Classification : 26D10, 42B20

Affiliations des auteurs :

André Guerra ¹ ; Bogdan Raiţă ²

¹ University of Oxford, Andrew Wiles Building, Woodstock Rd, Oxford OX2 6GG, United Kingdom
² Max Planck Institute for Mathematics in the Sciences, Inselstraße 22, 04103 Leipzig, Germany

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {On the necessity of the constant rank condition for $L^p$ estimates},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1091--1095},
     publisher = {Acad\'emie des sciences, Paris},
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     number = {9-10},
     year = {2020},
     doi = {10.5802/crmath.105},
     language = {en},
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André Guerra; Bogdan Raiţă. On the necessity of the constant rank condition for $L^p$ estimates. Comptes Rendus. Mathématique, Volume 358 (2020) no. 9-10, pp. 1091-1095. doi : 10.5802/crmath.105. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.105/

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