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Archiv der Mathematik

, Volume 107, Issue 1, pp 59–62 | Cite as

An elementary proof that the triharmonic Green function of an eccentric ellipse changes sign

  • Guido Sweers
Article

Abstract

The conjecture named after Boggio and Hadamard that a biharmonic Green function on convex domains is of fixed sign is known to be false. One might ask what happens for the triharmonic Green function on convex domains. On disks and balls it is known to be positive. We will show that also this Green function is not positive on some eccentric ellipse.

Mathematics Subject Classification

35G15 

Keywords

Triharmonic Green function Positivity 

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Mathematical InstituteCologne UniversityCologneGermany

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