Blowup analysis for two dimensional elliptic equations with exponential nonlinearities

具有指数非线性的二维椭圆型方程的爆破分析研究摘要张磊这个项目是研究一些与几何和物理问题有关的高度非线性的椭圆型方程。这些方程有一些非常奇异的项，它们的解也是非常奇异的。这项研究试图精确地描述解的奇性的性质，并将需要应用最近非线性方程研究的许多深入结果。对这些方程奇点的描述可能对物理学非常重要，并将有助于提供对相关场论的几何和分析理解。类似的方程也出现在一些生物现象的模型中，这些描述在那里可能是有用的。

Blowup Analysis for two-dimensional Elliptic Equations withExponential NonlinearitiesAbstract of Proposed ResearchLei Zhang This project is to study some highly nonlinear elliptic equations related to problems in geometry and physics. These equations have some very singular terms and their solutions also are quite singular. This research is to try to describe the nature of the singularities of the solutions precisely and will require the application of a many deep results from recent studies of non-linear equations. The descriptions of the singularities of these equations is likely to be quite important for physics and will help provide a geometrical and analytical understanding of the associated field theories. Similar equations also arise in some models of biological phenomena and these descriptions may be useful there.