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arXiv · 1512.05613

Doubling inequalities for the Lam\'e system with rough coefficients

Herbert Koch·Ching-Lung Lin·Jenn-Nan Wang
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Abstract

In this paper we study the local behavior of a solution to the Lam\'e system when the Lam\'e coefficients $\lambda$ and $\mu$ satisfy that $\mu$ is Lipschitz and $\lambda$ is essentially bounded in dimension $n\ge 2$. One of the main results is the \emph{local} doubling inequality for the solution of the Lam\'e system. This is a quantitative estimate of the strong unique continuation property. Our proof relies on Carleman estimates with carefully chosen weights. Furthermore, we also prove the \emph{global} doubling inequality, which is useful in some inverse problems.

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Herbert Koch, Ching-Lung Lin, Jenn-Nan Wang. 2015-12-17. Doubling inequalities for the Lam\'e system with rough coefficients. https://arxiv.org/abs/1512.05613

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