Blowup analysis for two dimensional elliptic equations with exponential nonlinearities

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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.