Sobolev不等式的Sharp梯度稳定性

IF 2.3 1区数学 Q1 MATHEMATICS

Duke Mathematical Journal Pub Date : 2020-03-09 DOI:10.1215/00127094-2022-0051

A. Figalli, Y. Zhang

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引用次数: 39

摘要

由于在变分演算和进化偏微分方程问题上的重要应用，近年来人们对函数/几何不等式的定量稳定性的理解越来越感兴趣，例如[3,2,8,27,28,21,9,22,29,18,10,6,7,11,13,19,23,35,26,14,16,17,20,25,30,31,24,33,34]，以及调查论文[15,26,17]。沿着这条研究路线，本文将研究经典Sobolev不等式的极小值的稳定性。

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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Sharp gradient stability for the Sobolev inequality

Motivated by important applications to problems in the calculus of variations and evolution PDEs, in recent years there has been a growing interest around the understanding of quantitative stability for functional/geometric inequalities, see for instance [3, 2, 8, 27, 28, 21, 9, 22, 29, 18, 10, 6, 7, 11, 13, 19, 23, 35, 26, 5, 14, 16, 17, 20, 25, 30, 31, 24, 33, 34], as well as the survey papers [15, 26, 17]. Following this line of research, in this paper we shall investigate the stability of minimizers to the classical Sobolev inequality.

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