1. EIGENVALUES AND EIGENFUNCTIONS OF DOUBLE LAYER POTENTIALS.
- Author
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YOSHIHISA MIYANISHI and TAKASHI SUZUKI
- Subjects
EIGENVALUES ,EIGENFUNCTIONS ,GEOMETRY ,EIGENANALYSIS ,MATHEMATICS - Abstract
Eigenvalues and eigenfunctions of two- and three-dimensional double layer potentials are considered. Let Ω be a C
2 bounded region in Rn (n = 2, 3). The double layer potential K : L2 (∂Ω) → L2 (∂Ω) is defined by (Kψ)(x) ≡ ∫∂ Ω ψ(y)·vy E(x, y) dsy , where E(x, y) = ∫1/2π log1/∣x-y∣ , if n = 2,1/π log1/∣x-y∣ , if n = 3, dsy is the line or surface element and vy is the outer normal derivative on ∂Ω. It is known that K is a compact operator on L2 (∂Ω) and consists of at most a countable number of eigenvalues, with 0 as the only possible limit point. This paper aims to establish some relationships among the eigenvalues, the eigenfunctions, and the geometry of ∂Ω. [ABSTRACT FROM AUTHOR]- Published
- 2017
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