Very weak solutions to the two-dimensional Monge-Ampere equation

被引：12

作者：

Cao, Wentao ^{[1
]}

Szekelyhidi, Laszlo, Jr. ^{[1
]}

机构：

[1] Univ Leipzig, Inst Math, D-04109 Leipzig, Germany

来源：

SCIENCE CHINA-MATHEMATICS | 2019年 / 62卷 / 06期

基金：

欧洲研究理事会;

关键词：

Monge-Ampere equation; convex integration; weak solutions; 35M10; 76B03; 76F02;

D O I：

10.1007/s11425-018-9516-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this short note we revisit the convex integration approach to constructing very weak solutions to the 2D Monge-Ampere equation with Holder-continuous first derivatives of exponent < 1/5. Our approach is based on combining the approach of Lewicka and Pakzad (2017) with a new diagonalization procedure which avoids the use of conformal coordinates, which was introduced by De Lellis et al. (2018) for the isometric immersion problem.

引用

页码：1041 / 1056

页数：16

共 26 条

[1] Well posedness of ODE's and continuity equations with nonsmooth vector fields, and applications [J].