報 告 人：蔣飛達 教授
報告題目：Purely interior estimates for a kind of two dimensional Monge-Ampere equations
報告時間：2025年6月4日（周三）上午10：00-11:00
報告地點：泉山17號樓101
主辦單位：數學與統計學院、數學研究院、科學技術研究院
報告人簡介：
蔣飛達，東南大學數學學院與丘成桐中心教授，博士生導師。研究領域為非線性偏微分方程。主要涉及Monge-Ampere型方程、k-Hessian型方程等完全非線性偏微分方程、及其在最優質量傳輸、幾何光學等問題中的應用；以及其他各類偏微分方程的理論和應用問題。已在Adv. Math.，Comm. Partial Differential Equations，Calc. Var. Partial Differential Equations，Arch. Ration. Mech. Anal.等權威數學期刊上發表30余篇學術論文。
報告摘要：
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.