Optimal three-ball inequalities and quantitative uniqueness for the Lam\'e system with Lipschitz coefficients

TL;DR

This paper establishes strong unique continuation for solutions to the Lamé system with Lipschitz coefficients, providing bounds on vanishing order and solving an open problem in the field.

Contribution

It proves the strong unique continuation property for the Lamé system with Lipschitz coefficients in any dimension, a previously unresolved issue.

Findings

Bound on the vanishing order of solutions

Strong unique continuation property established

Solves open problem for Lipschitz coefficients

Abstract

In this paper we study the local behavior of a solution to the Lam\'e system with \emph{Lipschitz} coefficients in dimension $n\ge 2$. Our main result is the bound on the vanishing order of a nontrivial solution, which immediately implies the strong unique continuation property. This paper solves the open problem of the strong uniqueness continuation property for the Lam\'e system with Lipschitz coefficients in any dimension.