Optimal three-ball inequalities and quantitative uniqueness for the Lamé system with Lipschitz coefficients

Abstract

In this article we study the local behavior of a solution to the Lamé system with Lipschitz coefficients in dimension n≥2. Our main result is the bound on the vanishing order of a nontrivial solution, which immediately implies the strong unique continuation property (SUCP). We solve the open problem of the SUCP for the Lamé system with Lipschitz coefficients in any dimension.