A priori estimates of Mizohata-Takeuchi type for the Navier-Lamé operator
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arXiv
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| Format: | Preprint |
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2025
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| author | Barceló, Juan Antonio Ruiz, Alberto Vilela, Mari Cruz Wright, Jim |
| author_facet | Barceló, Juan Antonio Ruiz, Alberto Vilela, Mari Cruz Wright, Jim |
| contents | The Mizohata-Takeuchi conjecture for the resolvent of the Navier-Lamé equation is a weighted estimate with weights in the so-called Mizohata-Takeuchi class for this operator when one approaches the spectrum (Limiting Absorption Principles). We prove this conjecture in dimensions 2 and 3 for weights with a radial majorant in the Mizohata-Takeuchi class. This result can be seen as an extension of the analogue for the Laplacian given in [8]. We also prove that radial weights in this class are not invariant for the Hardy-Littlewood maximal function, hence the methods in [6] used to extend estimates for the Laplacian to the Navier-Lamé case, do not work. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_10133 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A priori estimates of Mizohata-Takeuchi type for the Navier-Lamé operator Barceló, Juan Antonio Ruiz, Alberto Vilela, Mari Cruz Wright, Jim Analysis of PDEs Classical Analysis and ODEs The Mizohata-Takeuchi conjecture for the resolvent of the Navier-Lamé equation is a weighted estimate with weights in the so-called Mizohata-Takeuchi class for this operator when one approaches the spectrum (Limiting Absorption Principles). We prove this conjecture in dimensions 2 and 3 for weights with a radial majorant in the Mizohata-Takeuchi class. This result can be seen as an extension of the analogue for the Laplacian given in [8]. We also prove that radial weights in this class are not invariant for the Hardy-Littlewood maximal function, hence the methods in [6] used to extend estimates for the Laplacian to the Navier-Lamé case, do not work. |
| title | A priori estimates of Mizohata-Takeuchi type for the Navier-Lamé operator |
| topic | Analysis of PDEs Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2501.10133 |