Regularity for Partial Differential Equations

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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.