Quantitative strong unique continuation for the Lam\'e system with less regular coefficients

TL;DR

This paper establishes a quantitative strong unique continuation property for the Lamé system with less regular coefficients, specifically when the shear modulus is Lipschitz and the first Lamé parameter is essentially bounded, improving previous results.

Contribution

It extends prior work by proving the property under weaker regularity assumptions on the Lamé coefficients, specifically reducing the regularity requirement for rom Lipschitz to essentially bounded.

Findings

Proves quantitative strong unique continuation for the Lamé system with less regular coefficients.

Improves previous results by relaxing regularity assumptions on Lame9 coefficients.

Establishes new bounds applicable in elasticity theory.

Abstract

In this paper we prove a quantitative form of the strong unique continuation property for the Lam\'e system when the Lam\'e coefficients $\mu$ is Lipschitz and $\lambda$ is essentially bounded in dimension $n\ge 2$. This result is an improvement of our earlier result \cite{lin5} in which both $\mu$ and $\lambda$ were assumed to be Lipschitz.