Classification of blow-up limits for the sinh-Gordon equation. (English) Zbl 1449.35224

Jevnikar, Aleks; Wei, Juncheng; Yang, Wen

Differ. Integral Equ. 31, No. 9-10, 657-684 (2018).

Summary: 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 \[\Delta u+h_1e^u-h_2e^{-u}=0\qquad\text{in }B_1\subset\mathbb{R}^2.\] In particular, we get that the blow-up values are multiple of \(8\pi\). It generalizes the result of J. Jost et al. [Calc. Var. Partial Differ. Equ. 31, No. 2, 263–276 (2008; Zbl 1137.35061)] where the extra assumption \(h_1=h_2\) is crucially used.

MSC:

35J61	Semilinear elliptic equations
35R01	PDEs on manifolds
35B44	Blow-up in context of PDEs

Keywords:

compactness; differential geometry; Pohozaev identity; global Liouville equation

Citations:

Zbl 1137.35061