A priori estimates of Mizohata-Takeuchi type for the Navier-Lamé operator

2025/01/17 by Juan Antonio Barceló, Barceló, Juan Antonio, Alberto Ruiz +4 · 1 citation
Mathematics · #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2501.10133

openalex publication_date 2025/01/17 · openalex created_date 2025/01/21 · openalex updated_date 2026/07/31

Abstract

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.

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• A new addition theorem for the 3-D Navier-Lamé system and its application to the method of fundamental solutions

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