JournalscmhVol. 82 , No. 2DOI 10.4171/cmh/94

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

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.