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

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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.

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Change history

  • 20 December 2018

    The note added in proof of [1] is false.

  • 20 December 2018

    The note added in proof of [1] is false.

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Authors and Affiliations

  1. Mathematical Institute, Cologne University, Cologne, Germany

    Guido Sweers

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  1. Guido Sweers
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Correspondence to Guido Sweers.

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Sweers, G. An elementary proof that the triharmonic Green function of an eccentric ellipse changes sign. Arch. Math. 107, 59–62 (2016). https://doi.org/10.1007/s00013-016-0909-z

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  • DOI: https://doi.org/10.1007/s00013-016-0909-z

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