Doubling inequalities for the Lamé system with rough coefficients

Koch, Herbert; Lin, Ching-Lung; Wang, Jenn-Nan

doi:10.1090/proc/13175

Doubling inequalities for the Lamé system with rough coefficients
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by Herbert Koch, Ching-Lung Lin and Jenn-Nan Wang

Proc. Amer. Math. Soc. 144 (2016), 5309-5318

DOI: https://doi.org/10.1090/proc/13175

Published electronically: June 10, 2016

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Abstract:

In this paper we study the local behavior of a solution to the Lamé system when the Lamé 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 local doubling inequality for the solution of the Lamé 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 global doubling inequality, which is useful in some inverse problems.

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