We consider a generalization of the elliptic -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.
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André Guerra 1; Bogdan Raiţă 2
@article{CRMATH_2020__358_9-10_1091_0, author = {Andr\'e Guerra and Bogdan Rai\c{t}\u{a}}, 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}, volume = {358}, number = {9-10}, year = {2020}, doi = {10.5802/crmath.105}, language = {en}, }
TY - JOUR AU - André Guerra AU - Bogdan Raiţă TI - On the necessity of the constant rank condition for $L^p$ estimates JO - Comptes Rendus. Mathématique PY - 2020 SP - 1091 EP - 1095 VL - 358 IS - 9-10 PB - Académie des sciences, Paris DO - 10.5802/crmath.105 LA - en ID - CRMATH_2020__358_9-10_1091_0 ER -
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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