Strong unique continuation for the Lamé system with Lipschitz coefficients
The authors prove the strong unique continuation property (SUCP) for the equations of linear isotropic elasticity in \({\mathbb R}^2\). Extending previous results by \textit{G. Alexandrini} and \textit{A. Morassi} [Commun. Partial Differ. Equ. 26, 1787--1810 (2001; Zbl 1086.35016)], where a least \(C^{1,1}\)-coefficients must be assumed, they achieve (SUCP) in the case of Lipschitz coefficients. To this end they introduce a reduction to a first order system carefully avoiding differentiation of the coefficients. The resulting system has still some coupling in the principal part so (SUCP) cannot be inferred directly. Instead they give a two-step proof: Polynomial decay implies exponential decay which in turn implies vanishing in a neighbourhood.
scientific article; zbMATH DE number 2156236
scientific article