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Nonuniqueness of infinity ground states

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Abstract

In this paper, we construct a dumbbell domain for which the associated principal ∞-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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Authors and Affiliations

  1. Department of Mathematics, Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY, 10012-1185, USA

    Ryan Hynd

  2. Department of Mathematics, MIT, 2-339 77 Massachusetts Avenue, Cambridge, MA, 02139, USA

    Charles K. Smart

  3. Department of Mathematics, University of California Irvine, 410G Rowland Hall, Mail Code: 3875, Irvine, CA, 92697, USA

    Yifeng Yu

Authors
  1. Ryan Hynd
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  2. Charles K. Smart
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  3. Yifeng Yu
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Correspondence to Yifeng Yu.

Additional information

Communicated by O. Savin.

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Hynd, R., Smart, C.K. & Yu, Y. Nonuniqueness of infinity ground states. Calc. Var. 48, 545–554 (2013). https://doi.org/10.1007/s00526-012-0561-9

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  • DOI: https://doi.org/10.1007/s00526-012-0561-9

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