Mathematical Sciences: Nonlinear Partial Differential Equations with Applications to Geometric Analysis and Continuum Mechanics

该项目将支持对三个问题的调查 椭圆型偏微分方程 第一 问题是要获得尖锐的估计和精确的表达式， 特征值和分歧点。 第二个问题是， 光滑超曲面存在性定理 规定的平均曲率一般黎曼空间，和 第三个问题是建立存在定理， 具有指定初等对称函数的超曲面 主法线曲率。 这些问题来源于连续介质力学中的问题 微分几何 该项目的成果有 潜在的应用领域，如开发新的 材料和静态结构中的应力计算。

This project will support investigation of three problems concerning elliptic partial differential equations. The first problem is to obtain sharp estimates and exact expressions for eigenvalues and bifurcation points. The second problem is to establish existence theorems for smooth hypersurfaces with prescribed mean curvature in general Riemann spaces, and the third problem is to establish existence theorems for hypersurfaces with prescribed elementary symmetric function of the principal normal curvatures. These problems come from questions in Continuum Mechanics and Differential Geometry. Results from this project have potential applications in areas such as the development of new materials and the computation of stresses in static structures.