On the Nonexistence of Transmission Eigenvalues for Regions with Cavities

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.

Keywords:

• Helmholtz equation
• Scattering problem
• Transmission eigenvalues

Mathematics Subject Classification:

• 35J05
• 35P25
• 35R30

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.