The elastic wave equation of limited smoothness

2010/09/05 by Valeriy Brytik, Maarten V. de Hoop, Brytik, Valeriy +8
Computer Science · Mathematics · #35L51 #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #math.AP #msc:35L51

paper · pdf · doi:10.48550/arxiv.1009.0933

arxiv created 2010/09/05 · openalex publication_date 2010/09/05 · arxiv updated 2010/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish a decoupling result for the P and S waves of linear, isotropic elasticity, in the setting of twice-differentiable Lamé parameters. Precisely, we show that the P↔ S components of the wave propagation operator are regularizing of order one on L² data, by establishing the diagonalization of the elastic system modulo a L²-bounded operator. Effecting the diagonalization in the setting of twice-differentiable coefficients depends upon the symbol of the conjugation operator having a particular structure.

Citations

• Reflection of singularities of solutions to systems of differential equations
• Quantitative strong unique continuation for the Lamé system with less regular coefficients

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