Boundary integral formulations of eigenvalue problems for elliptic differential operators with singular interactions and their numerical approximation by boundary element methods

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Abstract

In this paper the discrete eigenvalues of elliptic second order differential operators in L 2 (R n), n ∈ N, with singular δ-and δ -interactions supported on hypersurfaces are stud-ied. We show the self-adjointness of these operators and derive equivalent formulations for the eigenvalue problems involving boundary integral operators. These formulations are suitable for the numerical computations of the discrete eigenvalues and the corresponding eigenfunctions by boundary element methods. We provide convergence results and show numerical examples.

Original languageEnglish
Article numberOaM-14-39
Pages (from-to)555-599
Number of pages45
JournalOperators and Matrices
Volume14
Issue number3
DOIs
Publication statusPublished - Sep 2020

Keywords

  • Boundary element method
  • Discrete eigenvalues
  • Elliptic differential operators
  • Integral operators
  • δ and δ -interaction

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory

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