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Curvature Estimates for the Level Sets of Solutions to the monge-Ampère equation det D^2u = 1

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Chinese Annals of Mathematics,Series B 2014年第6期35卷 895-906页

作者： Chuanqiang CHEN Xinan MA Shujun SHI Wu Wen-Tsun Key Laboratory of Mathematics University of Science and Technology of China School of Mathematical Sciences University of Science and Technology of China School of Mathematical Sciences Harbin Normal University

For the monge-Amp`ere equation det D2u = 1, the authors find new auxiliary curvature functions which attain their respective maxima on the boundary. Moreover, the upper bounded estimates for the Gauss curvature and th... 详细信息

关键词： Curvature estimates Level sets monge-ampere equation

Singular Solutions to monge-Ampère equation

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Analysis in Theory and Applications 2022年第2期38卷 121-127页

作者： Luis A.Caffarelli Yu Yuan Department of Mathematics The University of Texas at AustinAustinTX 78712USA University of Washington Department of MathematicsBox 354350SeattleWA 98195USA

We construct merely Lipschitz and C^(1,α)with rational α∈(0,1−2/n]viscosity solutions to the monge-ampere equation with constant right hand side.

关键词： monge-ampere equation

Derivative Estimates for the Solution of Hyperbolic Affine Sphere equation

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Communications in Mathematical Research 2015年第1期31卷 62-70页

作者： WU YA-DONG Rong Xiao-chun College of Mathematics and Information Science Jiangxi Normal University

Considering the hyperbolic affine sphere equation in a smooth strictly convex bounded domain with zero boundary values, the sharp derivative estimates of any order for its convex solution are obtained.

关键词： hyperbolic affine sphere monge-ampere equation derivative estimate

A Complete Characterization of Multivariate Normal Stable Tweedie Models through a monge ampere Property

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Acta Mathematica Sinica,English Series 2020年第11期36卷 1232-1244页

作者： Célestin C.KOKONENDJI Cyrille C.MOYPEMNA SEMBONA Khoirin NISA Laboratoire de Mathematiques de Besancon(LMB)-Universite Bourgogne Franche-Comte 16Route de Gray-25030 Besancon CedexErance Department of Mathematics and Informatics-University of Bangui B.P.908 BanguiCeretrl African Repusblic Departarert of Mathematics-Uriaersity of Lampung Jl.Prof.Dr.Soemantri Brodjonegoro No.1 Bandar Lampung 35145Indonesia

Extending normal gamma and normal inverse Gaussian models,multivariate normal stable Tweedie(NST)models are composed by a fixed univariate stable Tweedie variable having a positive value domain,and the remaining random variables given the fixed one are real independent Gaussian variables with the same variance equal to the fixed *** the framework of multivariate exponential families,the NST models are recently classified by their covariance matrices V(m)depending on the mean vector *** this paper,we prove the characterization of all the NST models through their determinants of V(m),also called generalized variance functions,which are power of only one component of *** result is established under the NST assumptions of monge-ampere property and *** completes the two special cases of NST,namely normal Poisson and normal gamma *** a matter of fact,it provides explicit solutions of particular monge-ampere equations in differential geometry.

关键词： Covariance matrix generalized variance function monge-ampere equation multivariateexponential family steepness

Weighted Endpoint Estimates for Maximal Commutators Associated with the Sections

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Acta Mathematica Sinica,English Series 2010年第8期26卷 1463-1474页

作者： Jie Cheng CHEN Yan Dan ZHANG Department of Mathematics Zhejiang University Hangzhou 310027 P. R. China

We prove endpoint estimates for maximal commutators for a class of singular integral operators related to the real analysis of the monge ampere equation.

关键词： Weighted inequalities maximal commutators monge-ampere equation the sharp maximal function

monge—ampere方程全局解的存在性

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Northeastern Mathematical Journal 1995年第4期11卷 401-406页

作者：鹿立江

In this peper. we study the existence of global positive solutions of monge-ampere equation in whole space R, and prove that the numbers of such solutions are infinite. And we abc discuss its limit properties.

关键词： Elliptic Differential equation monge-ampere equation Existence of the Solution