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,...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer-Verlag,
2016-10-19T17:40:40Z.
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| Subjects: | |
| Online Access: | Get fulltext |
| Summary: | 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. |
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