Three spheres inequalities and unique continuation for a three-dimensional Lam\'e system of elasticity with C^1 coefficients

TL;DR

This paper establishes quantitative three spheres inequalities and unique continuation properties for solutions to the three-dimensional Lamé system of elasticity with C^1 coefficients, extending understanding of elastic wave behavior.

Contribution

It provides the first proof of three spheres inequalities and strong unique continuation for the Lamé system with C^1 coefficients in three dimensions.

Findings

Proved three spheres inequalities for the Lamé system

Established strong unique continuation property

Extended results to systems with C^1 coefficients

Abstract

Assuming that the Lam\'{e} moduli $\mu$, $\lambda$ are $C^{\tiny{1}}$ and $n\geq2$, we prove quantitative estimates of a weak sense of strong unique continuation for thesolutions of the n-dimensional Lam\'{e} system of the form of three spheres inequalities.