Convergence for a Liouville equation
Li Ma, Juncheng Wei · Commentarii Mathematici Helvetici · 2001
In this paper, we study the asymptotic behavior of solutions of the Dirichlet problem for the Liouville equationΩ K(x)e u on a bounded smooth domain Ω in the plane as λ → 8mπ , where m = 1, 2, ... .The equation is also called the Mean Field Equation in Statistical Mechanics.By a result of H.Brezis and F.Merle, any solution sequence may have a finite number of bubbles.We give a necessary condition for the location of the bubble points.