论文标题
Neumann边界的$ c^0 $ -Convergence for Liouville方程式
The $C^0$-convergence at the Neumann boundary for Liouville equations
论文作者
论文摘要
在本文中，我们研究了具有指数neumann边界条件的Liouville型方程的一系列解决方案的爆炸分析。对于内部情况，即爆破点是一个内部点，li \ cite {li}给出了均匀的渐近估计值。后来，张\ cite {zhang}和gluck \ cite {gluck}通过使用移动平面或Liouville方程线性化版本的解决方案的解决方案的方法来改善Li的估计。如果序列在边界点爆炸，则Bao-Wang-Zhou \ cite {Bao-Wang-Zhou}证明了类似的渐近估计值\ cite {li}。在本文中，我们将在此边界爆破过程中证明$ C^0 $ - convergence。我们的方法不同于\ cite {zhang，gluck}。
In this paper, we study the blow-up analysis for a sequence of solutions to the Liouville type equation with exponential Neumann boundary condition. For interior case, i.e. the blow-up point is an interior point, Li \cite{Li} gave a uniform asymptotic estimate. Later, Zhang \cite{Zhang} and Gluck \cite{Gluck} improved Li's estimate in the sense of $C^0$-convergence by using the method of moving planes or classification of solutions of the linearized version of Liouville equation. If the sequence blows up at a boundary point, Bao-Wang-Zhou \cite{Bao-Wang-Zhou} proved a similar asymptotic estimate of Li \cite{Li}. In this paper, we will prove a $C^0$-convergence result in this boundary blow-up process. Our method is different from \cite{Zhang,Gluck}.
