报告题目： Entire solutions of Monge-Ampere equations with prescribed asymptotic behaviors

报告时间: 2018年11月16日14点40分-15点40分

报告地点: 数学院大会议室

报告人: 保继光教授 （北京师范大学）

内容摘要：We prove the existence of entire solutions of the Monge-Ampere equations with prescribed asymptotic behavior at infinity of the plane, which was left by Caffarelli-Li in 2003. The special difficulty of the problem in dimension two is due to the global logarithmic term in the asymptotic expansion of solutions at infinity. Furthermore, we give a PDE proof of the characterization of the space of solutions of the Monge-Ampere equation det with singular points, which was established by Galvez-Martinez-Mira in 2005. We also obtain the existence in higher dimensional cases with general right hand sides.

报告人简介: 北京师范大学数学学院二级教授，博士生导师. 享受国务院政府特殊津贴专家。现任教育部高等学校数学类专业教学指导委员会委员，数学与复杂系统教育部重点实验室副主任，中国数学会常务理事和基础教育工作委员会主任，中国少数民族数学教育专业委员会副理事长。其研究领域为非线性偏微分方程。在《Amer. J. Math.》、 《Trans. Amer. Math. Soc.》、 《Adv. Math.》、 《Arch. Ration. Mech. Anal.》、 《Calc. Var. Partial Differential Equations》、 《Ann. Henri Poincaré》、 《J. Funct. Anal.》、 《Indiana Univ. Math.》、 《J. Differ. Equations》和《Biomaterials》等国际顶级学术期刊发表论文70余篇。