Calculus of Variations and Geometric Measure Theory

A. Jevnikar - J. Wei - W. Yang

Classification of blow-up limits for the sinh-Gordon equation

created by jevnikar on 11 Feb 2016
modified on 16 Sep 2016


Accepted Paper

Inserted: 11 feb 2016
Last Updated: 16 sep 2016

Journal: Differential and Integral Equations
Year: 2016


Aim of the paper is to use a selection process and a careful study of the interaction of bubbling solutions to show a classification result for the blow-up values of the elliptic sinh-Gordon equation $\Delta u+h_1e^u-h_2e^{-u}=0 \mathrm{in} B_1\subset\mathbb{R}^2.$ In particular we get that the blow-up values are multiple of $8\pi.$ It generalizes the result of Jost, Wang, Ye and Zhou where the extra assumption $h_1 = h_2$ is crucially used.