1.授课专家 Instructor
Professor Lei Ni (University of California, San Diego)
2. 短课程介绍 Introduction
课程名： Monge-Ampere equations
摘要： This course is an introduction to the real and complex Monge-Ampere equations. We will discuss weak solutions, maximum principles, apriori estimates, and Liouville-type theorems of real and complex Monge-Ampere equations.
参考文献：
Figalli, Alessio. The Monge-Ampère equation and its applications. Zurich Lectures in Advanced Mathematics. European Mathematical Society, 2017.
先修课程和准备知识：
(1) Evans and Han-Lin: Parts on the weak solutions and viscosity solutions.
(2) Gilbarg-Trudinger: Parts on Krylov-Safanov estimate and fully nonlinear PDEs.
(3) Aubin: Parts on complex Monge-Ampere equations.
更多相关文献：
(1) Evans, Lawrence C.. Partial differential equations. Second edition. Graduate Studies in Mathematics, 19. American Mathematical Society, Providence, RI, 2010.
(2) Han, Qing; Lin, Fanghua. Elliptic partial differential equations. Second edition. Courant Lecture Notes in Mathematics, 1. Courant Institute of Mathematical Sciences, New York; American Mathematical Society, Providence, RI, 2011
(3) Gilbarg, David; Trudinger, Neil S.. Elliptic partial differential equations of second order. Reprint of the 1998 edition. Classics in Mathematics. Springer-Verlag, 2001.
(4) Aubin, Thierry. Some nonlinear problems in Riemannian geometry. Springer Monographs in Mathematics. Springer-Verlag, 1998.
3.授课时间与内容 Schedule and Summary of Topics
Time | Summary of topics |
05/25 Thu 10-11:30 AM | Lecture 1: Concept of weak solutions |
05/27 Sat 10-11:30 AM | Lecture 2: Maximum principle |
05/30 Tue 10-11:30 AM | Lecture 3: Pogorelov estimate |
06/01 Thu 10-11:30 AM | Lecture 4: A Liouville theorem |
06/03 Sat 10-11:30 AM | Lecture 5: Complex Monge-Ampere equations |
4. 授课地点 Course Link:
腾讯会议：627634279 密码：978305
对本次课程感兴趣的老师、同学可自行线上参加。如果出现网络等或其他意外故障，请大家及时访问此网页获得最新信息。
5. 联系人 Contact
杨波 boyang@xmu.edu.cn
叶老师，0592-2580036，tymath2@xmu.edu.cn
6. 课程资源