Nonuniqueness of infinity ground states

Abstract

In this paper, we construct a dumbbell domain for which the associated principal [infinity symbol]-eigenvalue is not simple. This gives a negative answer to the outstanding problem posed in Juutinen et al. (Arch Ration Mech Anal 148(2):89–105, 1999; The infinity Laplacian: examples and observations, 2001). It remains a challenge to determine whether simplicity holds for convex domains.