An elementary proof that the triharmonic Green function of an eccentric ellipse changes sign. (English) Zbl 1347.35094
Arch. Math. 107, No. 1, 59-62 (2016); correction ibid. 112, No. 2, 223-224 (2019).
Summary: 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 show that also this Green function is not positive on some eccentric ellipse.
MSC:
| 35J08 | Green’s functions for elliptic equations |
References:
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