Horizontal and Vertical Regularity of Elastic Wave Geometry

2025/11/20 by Ilmavirta, Joonas, Kirkkopelto, Pieti, Kykkänen, Antti
#14J81 #58J60 #74B05 #86A22 #Algebraic Geometry (math.AG) #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2511.16466

Abstract

The elastic properties of a material are encoded in a stiffness tensor field and the propagation of elastic waves is modeled by the elastic wave equation. We characterize analytic and algebraic properties a general anisotropic stiffness tensor field has to satisfy in order for Finsler-geometric methods to be applicable in studying inverse problems related to imaging with elastic waves.

Citations

• Lipschitz Stability of Travel Time Data
• Microlocal analysis of the X-ray transform in non-smooth geometry
• Tensor tomography on negatively curved manifolds of low regularity
• The geodesic ray transform on spherically symmetric reversible Finsler manifolds
• Quantitative unique continuation for the elasticity system with application to the kinematic inverse rupture problem
• Pestov identities and X-ray tomography on manifolds of low regularity
• Elastic Wave Near-Cloaking
• Determination of a compact Finsler manifold from its boundary distance map and an inverse problem in elasticity
• Integral geometry on manifolds with boundary and applications
• Direct and Inverse Elastic Scattering From Anisotropic Media
• The X-ray transform on a general family of curves on Finsler surfaces
• Rigidity properties of Anosov optical hypersurfaces

Related

• Reconstruction of anisotropic stiffness tensors from partial data around one polarization
• On constraints imposed on a transversely isotropic elasticity tensor
• Determination of the density in the linear elastic wave equation
• Reconstruction of a fully anisotropic elasticity tensor from knowledge of displacement fields
• Low-Regularity Local Well-Posedness for the Elastic Wave System