Regularity for Partial Differential Equations

DMS-0401261PI：Lihe Wang(爱荷华大学)题目：偏微分方程正则性本文主要研究椭圆型、抛物型偏微分方程正则理论及其水平面的正则性。提出了几何、流体力学和多个复变量的退化方程，并将随机介质方程与障碍物问题的性质联系起来。介绍了对这些问题的新方法和新认识。PI致力于解决纯数学问题、液晶问题和地质水下问题。所提出的研究将对广泛的跨学科课题具有重要意义。该中心积极参与博士后和研究生的培训和招聘工作。在爱荷华大学数学系，有大约100名来自全国和全球各地的毕业生。

Proposal DMS-0401261PI: Lihe Wang (University of Iowa)Title: Regularity for Partial Differential EquationsABSTRACTThis proposal is directed to the study of regularity theory of elliptic,parabolic partial differential equations and the study of the regularity properties of their level surfaces. Degenerate equations arising from geometry, fluid dynamics and several complex variables are also proposed.Equations with stochastic media are connected with properties of theobstacle problems. New methods and new understandings to these problems are introduced.The PI is working on problems from pure mathematics and on issues from liquid crystals and from geological underwater problems. The proposed research will be important for a wide interdisciplinary subjects. The PI is actively involved in the training and recruiting of post-doctors and graduate students. At the MathematicsDepartment of the University of Iowa, there is a student body about 100 graduatestudents from around the country and around the globe.