Translator Disclaimer
2019 Embedded eigenvalues for the Neumann-Poincare operator
Wei Li, Stephen P. Shipman
J. Integral Equations Applications 31(4): 505-534 (2019). DOI: 10.1216/JIE-2019-31-4-505

Abstract

The Neumann-Poincare operator is a boundary-integral operator associated with harmonic layer potentials. This article proves the existence of eigenvalues within the essential spectrum for the Neumann-Poincar\'e operator for certain Lipschitz curves in the plane with reflectional symmetry, when considered in the functional space in which it is self-adjoint. The proof combines the compactness of the Neumann-Poincare operator for curves of class $C^{2,\alpha }$ with the essential spectrum generated by a corner. Eigenvalues corresponding to even (odd) eigenfunctions are proved to lie within the essential spectrum of the odd (even) component of the operator when a $C^{2,\alpha }$ curve is perturbed by inserting a small corner.

Citation

Download Citation

Wei Li. Stephen P. Shipman. "Embedded eigenvalues for the Neumann-Poincare operator." J. Integral Equations Applications 31 (4) 505 - 534, 2019. https://doi.org/10.1216/JIE-2019-31-4-505

Information

Published: 2019
First available in Project Euclid: 6 February 2020

zbMATH: 07169459
MathSciNet: MR4060438
Digital Object Identifier: 10.1216/JIE-2019-31-4-505

Subjects:
Primary: 31A10

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

JOURNAL ARTICLE
30 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.31 • No. 4 • 2019
Back to Top