Nonuniqueness of infinity ground states

DOI10.1007/S00526-012-0561-9zbMATH Open1277.35272arXiv1205.6828OpenAlexW2085524377MaRDI QIDQ376599

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Publication date: 5 November 2013

Published in: (Search for Journal in Brave)

Abstract: In this paper, we construct a dumbbell domain for which the associated principle $infty$-eigenvalue is not simple. This gives a negative answer to the outstanding problem posed by Juutinen-Lindquivst-Manfredi ("The $infty$-eigenvalue problem", Arch. Ration. Mech. Anal. 148, 1999, no.2, 89-105). It remains a challenge to determine whether simplicity holds for convex domains.

Full work available at URL: https://arxiv.org/abs/1205.6828

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