Title： The interior regularity for solutions of the sigma_2

Speaker：邱国寰  （加拿大McGill大学）

Time：2018年1月11日   下午 16:30--17:30

Room：东区管理科研楼  数学科学学院1518室 

Abstract： Hessian equation is a longstanding problem. Heinz first derived this interior estimate in dimension two. For higher dimensional Monge-Ampere equations, Pogorelov constructed his famous counter-examples even for f constant and convex solutions.  Caffarelli-Nirenberg-Spruck studied more general fully nonlinear equations such as \sigma_{k} equations in their seminal work. And Urbas also constructed counter-examples with k greater than 3. The only unknown case is k=2. A major breakthrough was made by Warren-Yuan, they obtained a prior interior Hessian estimate for the equation \sigma_2=1 in dimension three. 

In this talk, I will present my recent work on how to deal this problem for a more general case in dimension three.