Bounds on positive interior transmission eigenvalues

Abstract

The paper contains lower bounds on the counting function of the positive eigenvalues of the interior transmission problem when the latter is elliptic. In particular, these bounds justify the existence of an infinite set of interior transmission eigenvalues and provide asymptotic estimates from above on the counting function for the large values of the wave number. They also lead to certain important upper estimates on the first few interior transmission eigenvalues. We consider the classical transmission problem as well as the case when the inhomogeneous medium contains an obstacle.

We corrected inaccuracies cost by the wrong sign in the Green formula (17). In particular, the sign in the definition of σwas changed

References in corpus (1)

• Remarks on interior transmission eigenvalues, Weyl formula and branching billiards

Cited by in corpus (12)

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• Elastic interior transmission eigenvalues and their computation via the method of fundamental solutions
• Weyl type bound on positive Interior Transmission Eigenvalues
• Interior transmission eigenvalue problems on compact manifolds with boundary conductivity parameters
• A Proof of Schiffer's Conjecture in Starlike Domain by Far-Field Patterns
• An Inverse Uniqueness in Interior Transmission Problem and Its Eigenvalue Tunneling in Penetrable Simple Domains
• A Near-Field Basis in Radially Symmetric Interior Transmission Problem