A SINGULAR DIRICHLET PROBLEM FOR THE MONGE-AMPÈRE TYPE EQUATION  

作　　者：Zhijun ZHANG Bo ZHANG 张志军;张博(School of Mathematics and Information Science,Yantai University,Yantai,264005,China)

机构地区：[1]School of Mathematics and Information Science,Yantai University,Yantai,264005,China

出　　处：《Acta Mathematica Scientia》2024年第5期1965-1983,共19页数学物理学报（B辑英文版）

基　　金：supported by Shandong Provincial NSF(ZR2022MA020).

摘　　要：We consider the singular Dirichlet problem for the Monge-Ampère type equation■=0,whereΩis a strictly convex and bounded smooth domain in■is positive and strictly decreasing in(0,∞)with■is positive inΩ.We obtain the existence,nonexistence and global asymptotic behavior of the convex solution to such a problem for more general b and g.Our approach is based on the Karamata regular variation theory and the construction of suitable sub-and super-solutions.

关 键 词：Monge-Ampère equation a singular boundary value problem the unique convex solution global asymptotic behavior 

分 类 号：O175[理学—数学]