Nonuniqueness of infinity ground states

Nonuniqueness of infinity ground states

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,...

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Bibliographic Details
Main Authors: Hynd, Ryan (Author), Yu, Yifeng (Author), Smart, Charles (Contributor)
Other Authors: Massachusetts Institute of Technology. Department of Mathematics (Contributor)
Format: Article
Language:English
Published: Springer-Verlag, 2016-10-19T17:40:40Z.
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Online Access:Get fulltext
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100 1 0 |a Massachusetts Institute of Technology. Department of Mathematics  |e contributor 
100 1 0 |a Smart, Charles  |e contributor 
700 1 0 |a Yu, Yifeng  |e author 
700 1 0 |a Smart, Charles  |e author 
245 0 0 |a Nonuniqueness of infinity ground states 
260 |b Springer-Verlag,   |c 2016-10-19T17:40:40Z. 
856 |z Get fulltext  |u http://hdl.handle.net/1721.1/104852 
520 |a 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. 
546 |a en 
655 7 |a Article 
773 |t Calculus of Variations and Partial Differential Equations 

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