A singular Monge-Ampère equation on unbounded domains

作     者：Huaiyu Jian You Li 

作者机构：Department of Mathematical Sciences Tsinghua University 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2018年第61卷第8期

页      面：1473-1480页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by National Natural Science Foundation of China(Grant Nos.11771237 and 41390452) 

主　　题：Dirichlet problem singular Monge-Ampere equation unbounded domain 

摘      要：In this paper, we study the Dirichlet problem for a singular Monge-Amp`ere type equation on unbounded domains. For a few special kinds of unbounded convex domains, we find the explicit formulas of the solutions to the problem. For general unbounded convex domain ?, we prove the existence for solutions to the problem in the space C∞(?) ∩ C(?). We also obtain the local C1/2-estimate up to the ?? and the estimate for the lower bound of the solutions.