论文标题
集中解决方案，以奇异规定的高斯和地球曲率问题
Concentration solutions to singularly prescribed Gaussian and geodesic curvatures problem
论文作者
论文摘要
我们考虑具有指数neumann边界条件的以下liouville型方程：$$-Δ\ tilde u = \ varepsilon^2 K（x） e^{\tilde u}, \quad x\in\partial D, $$ where $D\subset \mathbb R^2$ is the unit disc, $\varepsilon^2 K(x)$ and $\varepsilon κ(x)$ stand for the prescribed Gaussian curvature and the prescribed geodesic curvature of the boundary, respectively.如果$κ（x） + \ sqrt {k（x） +κ（x）^2} $（\ in \ partial d $）具有严格的局部极点点，这是指数Neumann边界问题的全新结果，我们将证明浓度解决方案的存在。
We consider the following Liouville-type equation with exponential Neumann boundary condition: $$ -Δ\tilde u = \varepsilon^2 K(x) e^{2\tilde u}, \quad x\in D, \qquad \frac{\partial \tilde u}{\partial n} + 1 = \varepsilon κ(x) e^{\tilde u}, \quad x\in\partial D, $$ where $D\subset \mathbb R^2$ is the unit disc, $\varepsilon^2 K(x)$ and $\varepsilon κ(x)$ stand for the prescribed Gaussian curvature and the prescribed geodesic curvature of the boundary, respectively. We prove the existence of concentration solutions if $κ(x) + \sqrt{K(x)+κ(x)^2}$ ($x\in\partial D$) has a strictly local extremum point, which is a total new result for exponential Neumann boundary problem.
