Asymptotic non-degeneracy of the solution to the Liouville–Gel’fand problem in two dimensions
Tomohiko Sato, Takashi Suzuki · Commentarii Mathematici Helvetici · 2007
In this paper we study the asymptotic non-degeneracy of the solution to the Liouville–Gel’fand problem − Δv = λ V (x )e^v \text{ in }Ω, \quad v = 0 \text{ on } ∂ Ω, where Ω ⊂ ℝ^2 is a smooth bounded domain, V (x ) is a positive-valued C^1(\bar Ω) function, and λ > 0 is a constant.