Counterexamples

Complete SolutionYear of origin: 2026

Posted online: 2026-08-06 09:04:17Z by Henrik Shahgholian

Cite as: S-260806.1

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Schiffer's conjecture

Let $u$ solve $\Delta u+k^2u=0$ in $K$, with $u=0$, $|\nabla u|=1$, on $\partial K$, where the latter is a compact Lipschitz domain in $\mathbb R^3$ Then $K$ is a ball.

Solution Description

Two counterexamples have been published online on arXiv. Probably would need verification.

  1. Article Is an originA computer-assisted counterexample to the planar Pompeiu and Schiffer conjectures

    arxiv.org, 2026arXiv

  2. Article Is an originCounterexamples to Schiffer's Conjecture

    arxiv.org, 2026arXiv

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  • Created at: 2026-08-06 09:04:17Z