Nonuniqueness of infinity ground states
Abstract
In this paper, we construct a dumbbell domain for which the associated principle ∞-eigenvalue is not simple. This gives a negative answer to the outstanding problem posed by Juutinen-Lindquivst-Manfredi ("The ∞-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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