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arXiv · 1602.02437

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

Aleks Jevnikar·Juncheng Wei·Wen Yang
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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 $$\Delta u+h_1e^u-h_2e^{-u}=0 \quad \mathrm{in}~B_1\subset\mathbb{R}^2.$$ 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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Aleks Jevnikar, Juncheng Wei, Wen Yang. 2016-02-07. Classification of blow-up limits for the sinh-Gordon equation. https://arxiv.org/abs/1602.02437

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