Some counterexamples to Alt–Caffarelli–Friedman monotonicity formulas in Carnot groups

IF 1 3区数学 Q1 MATHEMATICS

Annali di Matematica Pura ed Applicata Pub Date : 2024-07-29 DOI:10.1007/s10231-024-01490-8

Fausto Ferrari, Davide Giovagnoli

引用次数: 0

Abstract

In this paper we continue the analysis of an Alt–Caffarelli–Friedman (ACF) monotonicity formula in Carnot groups of step \(s >1\) confirming the existence of counterexamples to the monotone increasing behavior. In particular, we provide a sufficient condition that implies the existence of some counterexamples to the monotone increasing behavior of the ACF formula in Carnot groups. The main tool is based on the lack of orthogonality of harmonic polynomials in Carnot groups. This paper generalizes the results proved in Ferrari and Forcillo (Atti Accad Naz Lincei Rend Lincei Mat Appl 34(2):295–306, 2023).

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卡诺群中al - caffarelli - friedman单调公式的一些反例

在本文中，我们继续分析步长\(s >1\)的卡诺群中的一个Alt-Caffarelli-Friedman （ACF）单调公式，证实了单调递增行为的反例的存在性。特别地，我们提供了一个充分条件，证明ACF公式在卡诺群中单调递增性的反例存在。主要的工具是基于卡诺群中调和多项式缺乏正交性。本文推广了Ferrari和Forcillo （Atti Accad Naz Lincei Rend Lincei Mat应用34(2):295 - 306,2023）中证明的结果。

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

Annali di Matematica Pura ed Applicata 数学-数学

CiteScore

2.10

自引率

10.00%

发文量

审稿时长

>12 weeks

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