The inside–outside duality for elastic scattering problems

Abstract

In this article, we derive the inside–outside duality for two time-harmonic, elastic scattering problems. First, we consider a rigid scattering object inside an isotropic, homogeneous background medium and second, we consider a penetrable, inhomogeneous scattering object inside this background medium. For the first scattering problem, we make use of the particular behavior or certain eigenvalues of the corresponding far field operator to characterize interior Dirichlet eigenvalues of the negative Navier operator. Then we adapt this technique to determine interior transmission eigenvalues that correspond to the second scattering problem.

Keywords:

• Inside–outside duality
• interior transmission eigenvalues
• elastic scattering

AMS Subject Classifications:

• 34L25
• 74B05
• 35P15

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research of SP was supported through an exploratory project granted by the University of Bremen in the framework of its institutional strategy, funded by the excellence initiative of the federal and state governments of Germany.