Discreteness of Transmission Eigenvalues for Higher-Order Main Terms and Perturbations

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...

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Bibliographic Details
Main Authors García, Andoni, Vesalainen, Esa V, Zubeldia, Miren
Format Journal Article
LanguageEnglish
Published 17.12.2015
Subjects
Mathematics - Analysis of PDEs
Mathematics - Spectral Theory
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Summary: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.
DOI:10.48550/arxiv.1512.05580