R^2上对偶Minkowski问题的可解性  

The Solvability of Dual Minkowski Problem in R^2

作　　者：魏娜[1] Wei Na(School of Statistics and Mathematics,Zhongnan University of Economics and Law,Wuhan 430073)

机构地区：[1]中南财经政法大学统计与数学学院

出　　处：《数学物理学报（A辑）》2019年第6期1314-1322,共9页Acta Mathematica Scientia

基　　金：中央高校基本科研业务费专项资金(2722019PY053);湖北省自然科学基金(2019CFB570)~~

摘　　要：该文研究Sobolev空间W^1,4(S)中一类约束变分问题存在极小可达元,在∫Sg(θ)dθ>0条件下,该极小可达元是相应Euler-Lagrange方程u″+u=g(θ)/u(u^2+u′^2),θ∈S的严格正解.基于此,该文在R^2上证明了文献[Huang-Lutwak-Yang-Zhang.Acta Math,2016,216(2):325-338]提出的对偶Minkowski问题的可解性.In this paper,we study the existence of minimum of a constrained variational problem in the Sobolev space W1,4(S).If∫(S)g(θ)dθ>0,the minimum is a positive solution to the related Euler-Lagrange equation u″+u=g(θ)/u(u^2+u′^2),θ∈S.Based on this,we prove the solvability of the dual Minkowski problem in R^2 posed by Huang-Lutwak-Yang-Zhang[Acta Math,2016,216(2):325–338].

关 键 词：对偶Minkowski问题 非线性方程 变分方法 

分 类 号：O176[理学—数学]