Discreteness of transmission eigenvalues for higher-order main terms and perturbations

Research output: Contribution to journalArticle


  • Andoni García
  • Esa V. Vesalainen
  • Miren Zubeldia

Research units

  • University of the Basque Country
  • Basque Center for Applied Mathematics
  • University of Helsinki


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 neighborhood of the boundary of the underlying domain. The zeroth-order term must satisfy a suitable coercivity condition in a neighborhood of the boundary.


Original languageEnglish
Pages (from-to)2382-2398
Number of pages17
JournalSIAM Journal on Mathematical Analysis
Issue number4
Publication statusPublished - 2016
MoE publication typeA1 Journal article-refereed

    Research areas

  • Higher-order main terms, Higher-order perturbations, Inverse problems, Transmission eigenvalues

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