Nonuniqueness of infinity ground states
Author(s)Hynd, Ryan; Yu, Yifeng; Smart, Charles
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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.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Calculus of Variations and Partial Differential Equations
Hynd, Ryan, Charles K. Smart, and Yifeng Yu. “Nonuniqueness of Infinity Ground States.” Calculus of Variations and Partial Differential Equations, vol. 48, no. 3–4 (October 2012), pp. 545–554.
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