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Quantitative uniqueness estimate for the Maxwell system with Lipschitz anisotropic media


Authors: Tu Nguyen and Jenn-Nan Wang
Journal: Proc. Amer. Math. Soc. 140 (2012), 595-605
MSC (2010): Primary 35B60, 35Q61
DOI: https://doi.org/10.1090/S0002-9939-2011-11137-7
Published electronically: June 10, 2011
MathSciNet review: 2846328
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Abstract: We study quantitative uniqueness estimates for the time harmonic Maxwell system with Lipschitz anisotropic media. Our main results are a three-balls inequality and a minimal vanishing rate at a point of any nontrivial solution. The proof relies on a Carleman estimate with a divergence term.


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Additional Information

Tu Nguyen
Affiliation: Department of Mathematics, University of Washington, Box 354350, Seattle, Washington 98195-4350
Email: anhtu@math.washington.edu

Jenn-Nan Wang
Affiliation: Department of Mathematics, Taida Institute of Mathematics, NCTS (Taipei), National Taiwan University, Taipei 106, Taiwan
Email: jnwang@math.ntu.edu.tw

DOI: https://doi.org/10.1090/S0002-9939-2011-11137-7
Keywords: Maxwell system, three balls inequalities, Carleman estimate
Received by editor(s): November 25, 2010
Published electronically: June 10, 2011
Additional Notes: The first author was supported by NSF grant DMS-0856687.
The second author was supported in part by the National Science Council of Taiwan. This work was initiated when the second author visited the Department of Mathematics at the University of Washington in the summer of 2010. He would like to thank Professor Uhlmann for the kind invitation and the hospitality of the mathematics department.
Communicated by: Hart F. Smith
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.