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

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2019,（6）
• 页码范围: 1041-1056
• 页数: 16页
• 语种: 英文

摘要

In this short note we revisit the convex integration approach to constructing very weak solutions to the 2D Monge-Ampére equation with H(o)lder-continuous first derivatives of exponent β ＜ 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.