锥中Sobolev不等式的稳定性

IF 2.4 2区数学 Q1 MATHEMATICS

Journal of Differential Equations Pub Date : 2025-04-11 DOI:10.1016/j.jde.2025.113325

Giulio Ciraolo , Filomena Pacella , Camilla Chiara Polvara

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引用次数: 0

摘要

我们证明了Bianchi-Egnell型锥上的一个定量Sobolev不等式，它暗示了一个稳定性性质。我们的结果适用于任何锥，只要Sobolev商的极小值是非简并的。当最小值是经典气泡时，我们有更精确的结果。最后，我们证明了局部估计不足以得到定量Sobolev不等式的最优常数。

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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Stability for the Sobolev inequality in cones

We prove a quantitative Sobolev inequality in cones of Bianchi-Egnell type, which implies a stability property. Our result holds for any cone as long as the minimizers of the Sobolev quotient are nondegenerate. When the minimizers are the classical bubbles we have more precise results. Finally, we show that local estimates are not enough to get the optimal constant for the quantitative Sobolev inequality.

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来源期刊

Journal of Differential Equations 数学-数学

CiteScore

4.40

自引率

8.30%

发文量

543

审稿时长

9 months

期刊介绍： The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools. Research Areas Include: • Mathematical control theory • Ordinary differential equations • Partial differential equations • Stochastic differential equations • Topological dynamics • Related topics