关于p估计常秩条件的必要性

arXiv: Classical Analysis and ODEs Pub Date : 2020-07-01 DOI:10.5802/crmath.105

André Guerra, Bogdan Raiță

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引用次数: 15

摘要

我们考虑了适合于具有非平凡核的线性算子的椭圆L^p -估计的推广。舒伦伯格和威尔科克斯的经典结果。Mat. Pura apple。(4) 88: 229- 305,1971)表明，如果算子具有常秩，则估计成立。我们证明了这种估计的常秩条件的必要性。

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On the necessity of the constant rank condition forLpestimates

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. (4) 88: 229-305, 1971) 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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arXiv: Classical Analysis and ODEs

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