Differential and Integral Equations

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

Aleks Jevnikar, Juncheng Wei, and 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 $$ \Delta u+h_1e^u-h_2e^{-u}=0 \qquad \mathrm{in}~B_1\subset\mathbb R^2. $$ In particular, we get that the blow-up values are multiple of $8\pi.$ It generalizes the result of Jost, Wang, Ye and Zhou [20] where the extra assumption $h_1 = h_2$ is crucially used.

Article information

Source
Differential Integral Equations, Volume 31, Number 9/10 (2018), 657-684.

Dates
First available in Project Euclid: 13 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.die/1528855434

Mathematical Reviews number (MathSciNet)
MR3814561

Zentralblatt MATH identifier
06945776

Subjects
Primary: 35J61: Semilinear elliptic equations 35R01: Partial differential equations on manifolds [See also 32Wxx, 53Cxx, 58Jxx] 35B44: Blow-up

Citation

Jevnikar, Aleks; Wei, Juncheng; Yang, Wen. Classification of blow-up limits for the sinh-Gordon equation. Differential Integral Equations 31 (2018), no. 9/10, 657--684. https://projecteuclid.org/euclid.die/1528855434


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