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Nonuniqueness of infinity ground states

Author(s)
Hynd, Ryan; Yu, Yifeng; Smart, Charles
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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.
Date issued
2012-10
URI
http://hdl.handle.net/1721.1/104852
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
Calculus of Variations and Partial Differential Equations
Publisher
Springer-Verlag
Citation
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.
Version: Author's final manuscript
ISSN
0944-2669
1432-0835

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