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

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

2009-01-29

arxiv.org/abs/0901.4638v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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