Remarks on interior transmission eigenvalues, Weyl formula and branching billiards

Abstract

The paper contains the Weyl formula for the counting function of the interior transmission problem when the latter is parameter-elliptic. Branching billiard trajectories are constructed, and the second term of the Weyl asymptotics is estimated from above under some conditions on the set of periodic billiard trajectories.

two misprints (in (13) and (14)) are corrected

Cited by in corpus (9)

• Spectral analysis on interior transmission eigenvalues
• Applications of elliptic operator theory to the isotropic interior transmission eigenvalue problem
• Bounds on positive interior transmission eigenvalues
• Transmission eigenvalue-free regions
• Completeness of generalized transmission eigenstates
• Upper bound for the counting function of interior transmission eigenvalues
• Weyl asymptotics of the transmission eigenvalues for a constant index of refraction
• Weyl type bound on positive Interior Transmission Eigenvalues
• Homogenization approach for the transmission eigenvalue problem for periodic media and application to the inverse problem