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EIGENVALUES AND EIGENFUNCTIONS OF DOUBLE LAYER POTENTIALS.
- Source :
-
Transactions of the American Mathematical Society . Nov2017, Vol. 369 Issue 11, p8037-8059. 23p. - Publication Year :
- 2017
-
Abstract
- Eigenvalues and eigenfunctions of two- and three-dimensional double layer potentials are considered. Let Ω be a C2 bounded region in Rn (n = 2, 3). The double layer potential K : L2(∂Ω) → L2(∂Ω) is defined by (Kψ)(x) ≡ ∫ ∂ Ω ψ(y)·vyE(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]
- Subjects :
- *EIGENVALUES
*EIGENFUNCTIONS
*GEOMETRY
*EIGENANALYSIS
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 00029947
- Volume :
- 369
- Issue :
- 11
- Database :
- Academic Search Index
- Journal :
- Transactions of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 125135483
- Full Text :
- https://doi.org/10.1090/tran/6913