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The Essential Spectrum of the Neumann-Poincaré Operator on a Domain with Corners

Lookup NU author(s): Professor Mihai Putinar

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Abstract

Exploiting the homogeneous structure of a wedge in the complex plane, we compute the spectrum of the anti-linear Ahlfors–Beurling transform acting on the associated Bergman space. Consequently, the similarity equivalence between the Ahlfors–Beurling transform and the Neumann–Poincaré operator provides the spectrum of the latter integral operator on a wedge. A localization technique and conformal mapping lead to the first complete description of the essential spectrum of the Neumann–Poincaré operator on a planar domain with corners, with respect to the energy norm of the associated harmonic field.

Publication metadata

Author(s): Perfekt KM, Putinar M

Publication type: Article

Publication status: Published

Journal: Archive for Rational Mechanics and Analysis

Year: 2017

Volume: 223

Issue: 2

Pages: 1019-1033

Print publication date: 01/02/2017

Online publication date: 31/10/2016

Acceptance date: 22/09/2016

Date deposited: 07/11/2016

ISSN (print): 0003-9527

ISSN (electronic): 1432-0673

Publisher: Springer

URL: http://dx.doi.org/10.1007/s00205-016-1051-6

DOI: 10.1007/s00205-016-1051-6

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