Global C2,α estimates for the Monge-Ampère equation on polygonal domains in the plane

IF 1.7 1区数学 Q1 MATHEMATICS

American Journal of Mathematics Pub Date : 2023-01-25 DOI:10.1353/ajm.2023.0004

N. Le, O. Savin

引用次数: 3

Abstract

Abstract:We classify global solutions of the Monge-Amp\\`ere equation $\\det D^2 u=1$ on the first quadrant in the plane with quadratic boundary data. As an application, we obtain global $C^\{2,\\alpha\}$ estimates for the non-degenerate Monge-Amp\\`ere equation in convex polygonal domains in $\\Bbb\{R\}^2$ provided a globally $C^2$, convex strict subsolution exists.

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平面多边形域上Monge-AmpeÉre方程的全局C2，α估计

摘要：我们用二次边界数据对平面第一象限上的Monge-Amp方程$\det D^2 u=1$的全局解进行了分类。作为一个应用，我们得到了$Bbb\{R\}^2$中凸多边形域中非退化Monge-Amp\` ere方程的全局$C^\{2，\\alpha\}$估计，前提是存在全局$C^2$凸严格亚解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

American Journal of Mathematics 数学-数学

CiteScore

3.20

自引率

0.00%

发文量

审稿时长

24 months

期刊介绍： The oldest mathematics journal in the Western Hemisphere in continuous publication, the American Journal of Mathematics ranks as one of the most respected and celebrated journals in its field. Published since 1878, the Journal has earned its reputation by presenting pioneering mathematical papers. It does not specialize, but instead publishes articles of broad appeal covering the major areas of contemporary mathematics. The American Journal of Mathematics is used as a basic reference work in academic libraries, both in the United States and abroad.