Discreteness of Transmission Eigenvalues for Higher-Order Main Terms and Perturbations
Abstract
In this paper we extend Sylvester's approach via upper triangular compact operators to establish the discreteness of transmission eigenvalues for higher-order main terms and higher-order perturbations. The coefficients of the perturbations must be sufficiently smooth and the coefficients of the higher-order terms of the perturbation must vanish in a neighbourhood of the boundary of the underlying domain. The zeroeth order term must satisfy a suitable coercivity condition in a neighbourhood of the boundary.
- Publication:
-
arXiv e-prints
- Pub Date:
- December 2015
- DOI:
- 10.48550/arXiv.1512.05580
- arXiv:
- arXiv:1512.05580
- Bibcode:
- 2015arXiv151205580G
- Keywords:
-
- Mathematics - Spectral Theory;
- Mathematics - Analysis of PDEs;
- 35J40;
- 35P30;
- 35P25
- E-Print:
- 19 pages