An expository survey on the recent development of mean field equations
Resource
Discrete and Continuous Dynamical Systems 19 (2): 387-410
Journal
Discrete and Continuous Dynamical Systems
Pages
387-410
Date Issued
2007
Date
2007
Author(s)
Lin, C.-S.
Abstract
We consider mean field equations: Δu + ρ(heu/ ∫Mheu-1) = 0 on M, where M is a compact Riemann surface with area 1, h is a positive continuous function and ρ is a constant, or {Δu+ρheu/∫Ωhe u=0 in Ω, u=0 on ∂Ω where Ω is a bounded C1 domain of ℝ2. In this paper, we give a short survey on the uniqueness problem, find sharper estimates of bubbling solutions and count the topological degree of solutions.
Type
journal article
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