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Doubling inequalities for the Lamé system with rough coefficients


Authors: Herbert Koch, Ching-Lung Lin and Jenn-Nan Wang
Journal: Proc. Amer. Math. Soc. 144 (2016), 5309-5318
MSC (2010): Primary 35J47
DOI: https://doi.org/10.1090/proc/13175
Published electronically: June 10, 2016
MathSciNet review: 3556273
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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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Additional Information

Herbert Koch
Affiliation: Mathematisches Institut, Universität Bonn, Endenicher Allee 60, D-53115 Bonn, Germany
Email: koch@math.uni-bonn.de

Ching-Lung Lin
Affiliation: Department of Mathematics and Research Center for Theoretical Sciences, NCTS, National Cheng-Kung University, Tainan 701, Taiwan
Email: cllin2@mail.ncku.edu.tw

Jenn-Nan Wang
Affiliation: Institute of Applied Mathematical Sciences, NCTS, National Taiwan University, Taipei 106, Taiwan
Email: jnwang@math.ntu.edu.tw

DOI: https://doi.org/10.1090/proc/13175
Keywords: Elliptic systems, doubling, Carleman inequalities, quantitative uniqueness
Received by editor(s): January 8, 2016
Received by editor(s) in revised form: February 24, 2016
Published electronically: June 10, 2016
Additional Notes: The first author was partially supported by the DFG through SFB 1060
The second author was partially supported by the Ministry of Science and Technology of Taiwan
The third author was partially supported by MOST102-2115-M-002-009-MY3
Communicated by: Joachim Krieger
Article copyright: © Copyright 2016 American Mathematical Society

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