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20180111The interior regularity for solutions of the sigma_2
20180111The interior regularity for solutions of the sigma_2
教师介绍

本讲教师:邱国寰
所属学科:理科
人  气:135

课程介绍
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.

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