A concavity condition for existence of a negative value in Neumann-Poincaré spectrum in three dimensions

Ji, Yong-Gwan; Kang, Hyeonbae

doi:10.1090/proc/14467

A concavity condition for existence of a negative value in Neumann-Poincaré spectrum in three dimensions
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by Yong-Gwan Ji and Hyeonbae Kang PDF

Proc. Amer. Math. Soc. 147 (2019), 3431-3438 Request permission

Abstract:

It is proved that if a bounded domain in three dimensions satisfies a certain concavity condition, then the Neumann-Poincaré operator on either the boundary of the domain or its inversion in a sphere has a negative value in its spectrum. The concavity condition is quite simple, and is satisfied if there is a point on the boundary at which the Gaussian curvature is negative.

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