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

Abstract

In this paper we study the local behavior of a solution to the Lamé 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 Lamé system with Lipschitz coefficients in any dimension.

References in corpus (2)

• Quantitative uniqueness for the power of Laplacian with singular coefficients
• Quantitative uniqueness for second order elliptic operators with strongly singular coefficients

Cited by in corpus (4)

• Dislocations in a layered elastic medium with applications to fault detection
• Resolvent estimates for the Lamé operator and failure of Carleman estimates
• Unique continuation property with partial information for two-dimensional anisotropic elasticity systems
• Stable determination of a Lamé coefficient by one internal measurement of displacement