Back to Search
Start Over
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 C<superscript>2</superscript> bounded region in R<superscript>n</superscript> (n = 2, 3). The double layer potential K : L<superscript>2</superscript>(∂Ω) → L<superscript>2</superscript>(∂Ω) is defined by (Kψ)(x) ≡ ∫<subscript> ∂ Ω</subscript> ψ(y)·v<subscript>y</subscript>E(x, y) ds<subscript>y</subscript>, where E(x, y) = ∫<subscript>1/2π log1/∣x-y∣ </subscript>, if n = 2, <superscript>1/π log1/∣x-y∣ </superscript>, if n = 3, ds<subscript>y</subscript> is the line or surface element and v<subscript>y</subscript> is the outer normal derivative on ∂Ω. It is known that K is a compact operator on L<superscript>2</superscript>(∂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 :
- Complementary Index
- Journal :
- Transactions of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 125135483
- Full Text :
- https://doi.org/10.1090/tran/6913