Regularity for Partial Differential Equations

题目：偏微分方程的正则性。摘要本课题主要研究椭圆型、抛物型偏微分方程的正则性理论及其水平面的正则性。还提出了由几何、流体力学和几个复杂变量引起的退化方程。随机介质方程与障碍问题的性质相联系。介绍了解决这些问题的新方法和新认识。PI正在研究纯数学问题、液晶问题和水下地质问题。所提出的研究将对广泛的跨学科学科具有重要意义。PI积极参与博士后和研究生的培训和招聘。在爱荷华大学数学系，有一个大约100名研究生的学生团体，他们来自全国和世界各地。

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.