半空间中monge - ampantere方程解在无穷远处的高阶展开

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications Pub Date : 2025-08-06 DOI:10.1016/j.na.2025.113912

Lichun Liang

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引用次数: 0

摘要

本文研究了平面边界上具有Dirichlet边界条件的半空间中monge - ampatire方程黏性解的渐近性质。通过开尔文变换，我们用原点附近的一个函数来描述渐近余数。该函数在偶维上在原点附近是光滑的，但在奇维上只有Cn−1，α (0<α<1)。

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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Higher order expansion at infinity of solutions for Monge–Ampère equations in the half space

In this paper, we investigate the asymptotic behavior of viscosity solutions for Monge–Ampère equations in the half space with a Dirichlet boundary condition on the flat boundary. Via the Kelvin transform, we characterize the asymptotic remainders by a single function near the origin. Such a function is smooth in the neighborhood of the origin in even dimension, but only

C^{n - 1, α}

(0 < α < 1)

in odd dimension.

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来源期刊

Nonlinear Analysis-Theory Methods & Applications 数学-数学

CiteScore

3.30

自引率

0.00%

发文量

265

审稿时长

60 days

期刊介绍： Nonlinear Analysis focuses on papers that address significant problems in Nonlinear Analysis that have a sustainable and important impact on the development of new directions in the theory as well as potential applications. Review articles on important topics in Nonlinear Analysis are welcome as well. In particular, only papers within the areas of specialization of the Editorial Board Members will be considered. Authors are encouraged to check the areas of expertise of the Editorial Board in order to decide whether or not their papers are appropriate for this journal. The journal aims to apply very high standards in accepting papers for publication.