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

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.