报告题目 (Title)：Green's function, Sobolev inequality and regularity of the linearized complex Monge-Ampere equation
中文标题: 线性化复Monge-Ampere方程的Green函数、Sobolev不等式和正则性
报告人 (Speaker)：周斌（北京大学）
报告时间 (Time)：2023年6月19日(周一) 15:30-16:30
报告地点 (Place)：宝山校区D108
邀请人(Inviter)：席东盟、李晋、张德凯
报告摘要：Let u be a smooth, strictly plurisubharmonic function on a bounded domain. We will discuss the regularity of solution to the linearized complex Monge-Ampere and Hessian equations. First, we establish a new Sobolev inequality when the complex Monge-Ampere operator of is bounded from above and below. Then by Moser's iteration with the new Sobolev inequality, we obtain an Harnack inequality for the linearized complex Monge-Ampere.