Advances in Differential Equations

On the asymptotic analysis of $H$-systems. I. Asymptotic behavior of large solutions

Takeshi Isobe

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Let $\Omega\subset\mathbb R^2$ be a bounded domain, $\gamma\in C^{3,\alpha}(\partial\Omega;\mathbb R^3 )$ $(0 <\alpha <1)$ and $H>0$. We consider the asymptotic behavior of large solutions of an $H$-system $$\Delta u=2Hu_{x_1}\wedge u_{x_2}\quad\text{in $\Omega$}, \qquad u=\gamma\quad \text{on $\partial\Omega$}$$ as $H\to 0$ or as $\gamma\to 0$. We show that large solutions blow up at exactly one point in $\Omega$. The exact blow-up rate and location of blow-up point are studied.

Article information

Adv. Differential Equations, Volume 6, Number 5 (2001), 513-546.

First available in Project Euclid: 2 January 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35B40: Asymptotic behavior of solutions
Secondary: 35J50: Variational methods for elliptic systems 35J60: Nonlinear elliptic equations


Isobe, Takeshi. On the asymptotic analysis of $H$-systems. I. Asymptotic behavior of large solutions. Adv. Differential Equations 6 (2001), no. 5, 513--546.

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