Three remarks on mean field equations

Li Ma

Vol. 242 (2009), No. 1, 167–171

DOI: 10.2140/pjm.2009.242.167

Abstract

We prove the Liouville theorem for the mean field equation (also called the conformal curvature equation) in ℝ², an a priori bound for solutions of the mean field equation on the negative part of indefinite nonlinearity, and the symmetry property of mean field equation on an annulus with zero Dirichlet boundary condition.

Keywords

mean field equation, conformal curvature, indefinite nonlinearity, moving sphere method, Liouville theorem

Mathematical Subject Classification 2000

Primary: 35J60

Secondary: 53C21, 58J05

Milestones

Received: 3 September 2008

Revised: 1 February 2009

Accepted: 3 April 2009

Published: 1 September 2009