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

Abstract

The aim of this 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 $$\Delta u+h_1{e}^u-h_2{e}^{-u}=0\mathrm{in}{B}_1\subset {\mathbb{R}}^2.$$ In particular we get that the blow-up values are multiple of $8\pi .$ It generalizes the result of Jost, Wang, Ye and Zhou \cite{jwyz} where the extra assumption $h_1=h_2$ is crucially used.

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