A quantitative result for the k-Hessian equation

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications Pub Date : 2025-02-19 DOI:10.1016/j.na.2025.113776

Alba Lia Masiello , Francesco Salerno

引用次数: 0

Abstract

In this paper, we study a symmetrization that preserves the mixed volume of the sublevel sets of a convex function, under which, a Pólya–Szegő type inequality holds. We refine this symmetrization to obtain a quantitative improvement of the Pólya–Szegő inequality for the

k

-Hessian integral, and, with similar arguments, we show a quantitative inequality for the comparison proved by Tso (1989) for solutions to the

k

-Hessian equation.

As an application of the first result, we prove a quantitative version of the Faber–Krahn and Saint-Venant inequalities for these equations.

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k-Hessian方程的定量结果

本文研究了一种保留凸函数子水平集混合体积的对称性，在这种对称性下，一个Pólya-Szegő型不等式成立。我们改进了这种对称性，得到了k-Hessian积分Pólya-Szegő不等式的一个定量改进，并且，用类似的论据，我们展示了由Tso（1989）证明的k-Hessian方程解的比较的一个定量不等式。作为第一个结果的应用，我们证明了这些方程的Faber-Krahn不等式和Saint-Venant不等式的一个定量版本。

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

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.