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Communications in Partial Differential Equations Volume 36, 2011 - Issue 8
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Original Articles

On the Nonexistence of Transmission Eigenvalues for Regions with Cavities

Guozheng Yan Faculty of Mathematics and Statistics, Central China Normal University, Wuhan, ChinaCorrespondence[email protected]
&
Mao Yao Faculty of Mathematics and Statistics, Central China Normal University, Wuhan, China
Pages 1510-1519 | Received 15 Sep 2010, Accepted 25 Jan 2011, Published online: 11 Aug 2011
 
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Abstract

We consider the interior transmission problem when the inhomogeneous medium has a cavity region. In this case we establish the Fredholm property for this problem and show that there does not exist a transmission eigenvalue under a new condition.

Mathematics Subject Classification:

Acknowledgments

This research is supported by NSFC grant No.10871080. It is also supported in part by grants from Ministry of Education of the People's Republic of China (No.107081), and Hubei Key Laboratory of Math. and Phy.

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