JournalscmhVol. 82, No. 2pp. 353–369

Asymptotic non-degeneracy of the solution to the Liouville–Gel’fand problem in two dimensions

  • Tomohiko Sato

    Osaka University, Japan

  • Takashi Suzuki

    Osaka University, Japan
Asymptotic non-degeneracy of the solution to the Liouville–Gel’fand problem in two dimensions cover
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Abstract

In this paper we study the asymptotic non-degeneracy of the solution to the Liouville–Gel’fand problem

− Δv = λ V (x )ev in Ω,   v = 0 on ∂ Ω,

where Ω ⊂ ℝ2 is a smooth bounded domain, V (x ) is a positive-valued C1(Ω) function, and λ  > 0 is a constant.

Cite this article

Tomohiko Sato, Takashi Suzuki, Asymptotic non-degeneracy of the solution to the Liouville–Gel’fand problem in two dimensions. Comment. Math. Helv. 82 (2007), no. 2, pp. 353–369

DOI 10.4171/CMH/94