2015年几何暑期学校Introduction to regularity theory of second order parabolic equations
Professor of Department of Mathematics ，University of California Riverside RESEARCH INTERESTS: Partial Differential Equations, Geometric Analysis Recent topics of study: 1. parabolic equations and systems with singular coefficients, Navier-Stokes system, e.g., 2. heat kernel estimates in various settings, 3. Ricci flow, 4. blow up phenomenon of parabolic and wave equations.
摘要：We will start with basic De Giorgi-Nash-Moser results for second order linear parabolic equations and there extensions to systems. Then we will discuss their extensions to Ricci flow and axially symmetric Navier-Stokes equations. New counter intuitive results such as backward in time regularity for the former and criticality for the later will be described. The course is accessible to graduate and advanced undergraduate students.