報(bào) 告 人：蔣飛達(dá) 教授

報(bào)告題目：Purely interior estimates for a kind of two dimensional Monge-Ampere equations

報(bào)告時(shí)間：2025年6月4日（周三）上午10：00-11:00

報(bào)告地點(diǎn)：泉山17號(hào)樓101

主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院、數(shù)學(xué)研究院、科學(xué)技術(shù)研究院

報(bào)告人簡(jiǎn)介：

蔣飛達(dá)，東南大學(xué)數(shù)學(xué)學(xué)院與丘成桐中心教授，博士生導(dǎo)師。研究領(lǐng)域?yàn)榉蔷€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(yōu)質(zhì)量傳輸、幾何光學(xué)等問(wèn)題中的應(yīng)用；以及其他各類偏微分方程的理論和應(yīng)用問(wèn)題。已在Adv. Math.，Comm. Partial Differential Equations，Calc. Var. Partial Differential Equations，Arch. Ration. Mech. Anal.等權(quán)威數(shù)學(xué)期刊上發(fā)表30余篇學(xué)術(shù)論文。

報(bào)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.