Mathematical Sciences: Regularity and Singularity in Constrained Variational Problems

首席研究员将在莱斯大学继续他在约束变分问题上的工作，作为明尼苏达大学一个小组项目的一部分(DMS-8718881)。需要解决的具体问题包括调和映射、几何测度论、偏微分方程式和力学。首席研究员将研究极小化问题、静态问题和动态问题解的正则性和奇异性。首席研究员将使用约束变分技术来解决液晶研究中出现的问题。解决这类问题的技术可以追溯到18世纪拉格朗日乘子的发明。此技术可用于在曲面上找到距离给定点最远的点。

The principal investigator will continue his work on constrained variational problems, while at Rice University, as part of a group project based at the University of Minnesota (DMS-8718881). The specific problems to be addressed lie in the areas of harmonic mappings, geometric measure theory, partial differential equations, and mechanics. The principal investigator will study the regularity and singularity of solutions of minimizing, stationary, and dynamic problems. Constrained variational techniques will be used by the principal investigator to solve problems arising from the study of liquid crystals. Techniques for the solution of such problems date back to the eighteenth century with the invention of Lagrange Multipliers. This technique can be used to find the point on a surface which is farthest from a given point.