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arXiv · 1205.6828

Nonuniqueness of infinity ground states

Ryan Hynd·Charles K. Smart·Yifeng Yu
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Abstract

In this paper, we construct a dumbbell domain for which the associated principle $\infty$-eigenvalue is not simple. This gives a negative answer to the outstanding problem posed by Juutinen-Lindquivst-Manfredi ("The $\infty$-eigenvalue problem", Arch. Ration. Mech. Anal. 148, 1999, no.2, 89-105). It remains a challenge to determine whether simplicity holds for convex domains.

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Ryan Hynd, Charles K. Smart, Yifeng Yu. 2012-05-30. Nonuniqueness of infinity ground states. https://arxiv.org/abs/1205.6828

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