右手边是多项式生长的monge - ampantere方程

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications Pub Date : 2025-05-28 DOI:10.1016/j.na.2025.113849

Beomjun Choi , Kyeongsu Choi , Soojung Kim

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引用次数: 0

摘要

本文研究了一类二维monge - ampantere方程的正则性及其解的增长率。利用这一分析，我们证明了高斯曲率次仿射临界幂流的翻译者是光滑的、严格凸的完整图。这些图表显示了特定的增长率，仅取决于流量的功率。

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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Monge–Ampère equations with right-hand sides of polynomial growth

We study the regularity and the growth rates of solutions to two-dimensional Monge–Ampère equations with the right-hand side exhibiting polynomial growth. Utilizing this analysis, we demonstrate that the translators for the flow by sub-affine-critical powers of the Gauss curvature are smooth, strictly convex entire graphs. These graphs exhibit specific growth rates that depend solely on the power of the flow.

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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.