报 告 人：蒋飞达 教授
报告题目：Purely interior estimates for a kind of two dimensional Monge-Ampere equations
报告时间：2025年6月4日（周三）上午10：00-11:00
报告地点：泉山17号楼101
主办单位：数学与统计学院、数学研究院、科学技术研究院
报告人简介：
蒋飞达，东南大学数学学院与丘成桐中心教授，博士生导师。研究领域为非线性偏微分方程。主要涉及Monge-Ampere型方程、k-Hessian型方程等完全非线性偏微分方程、及其在最优质量传输、几何光学等问题中的应用；以及其他各类偏微分方程的理论和应用问题。已在Adv. Math.，Comm. Partial Differential Equations，Calc. Var. Partial Differential Equations，Arch. Ration. Mech. Anal.等权威数学期刊上发表30余篇学术论文。
报告摘要：
In this talk, we discuss a kind of fully nonlinear equations of Monge-Ampere type, which can be applied to problems arising in optimal transport, geometric optics and conformal geometry. When the coefficient of the regular term has positive lower bound, the purely interior Hessian estimate is already known for higher dimensional case. When the coefficient of the regular term is equal to zero, singular solutions can be constructed for $n\ge 3$, while the purely interior Hessian estimate is obtained for $n=2$ case. As a byproduct, anew and simpleproofof the purely interior Hessianestimate for the two dimensional standard Monge-Ampere equation is provided.