On a fractional boundary version of Talenti’s inequality in the unit ball

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications Pub Date : 2025-09-02 DOI:10.1016/j.nonrwa.2025.104482

Yassin El Karrouchi, Tobias Weth

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引用次数: 0

Abstract

Inspired by recent work of Ferone and Volzone (2021), we derive sufficient conditions for the validity and non-validity of a boundary version of Talenti’s comparison principle in the context of Dirichlet–Poisson problems for the fractional Laplacian

{(- Δ)}^{s}

in the unit ball

Ω = B_{1} (0) \subset R^{N}

s \in (0, 1)

. In particular, our results imply a universal failure of the classical pointwise Talenti inequality in the fractional radial context. In contrast, a boundary Talenti type inequality holds for radial functions in the higher order case

s > 1

查看原文本刊更多论文

单位球中Talenti不等式的分数边界形式

受Ferone和Volzone（2021）最近工作的启发，我们在Dirichlet-Poisson问题的背景下，为单位球Ω=B1(0)∧RN, s∈(0,1)中的分数阶拉普拉斯算子（−Δ）s导出了Talenti比较原理的边界版本的有效性和非有效性的充分条件。特别地，我们的结果暗示了经典的点向Talenti不等式在分数径向环境中的普遍失效。相反，在高阶情况下径向函数的边界Talenti型不等式成立。

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-Real World Applications 数学-应用数学

CiteScore

3.80

自引率

5.00%

发文量

176

审稿时长

59 days

期刊介绍： Nonlinear Analysis: Real World Applications welcomes all research articles of the highest quality with special emphasis on applying techniques of nonlinear analysis to model and to treat nonlinear phenomena with which nature confronts us. Coverage of applications includes any branch of science and technology such as solid and fluid mechanics, material science, mathematical biology and chemistry, control theory, and inverse problems. The aim of Nonlinear Analysis: Real World Applications is to publish articles which are predominantly devoted to employing methods and techniques from analysis, including partial differential equations, functional analysis, dynamical systems and evolution equations, calculus of variations, and bifurcations theory.