高斯法布尔-克拉恩不等式的稳定性

IF 1 3区数学 Q1 MATHEMATICS

Annali di Matematica Pura ed Applicata Pub Date : 2024-03-30 DOI:10.1007/s10231-024-01441-3

Alessandro Carbotti, Simone Cito, Domenico Angelo La Manna, Diego Pallara

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引用次数: 0

摘要

我们证明了(Betta et al. in Z. Angew. Math. Phys. 58:37-52, 2007)中针对奥恩斯坦-乌伦贝克算子的第一个狄利克特特征值所证明的高斯法伯-克拉恩型不等式的定量版本，用高斯弗兰克尔不对称来估计赤字。不出所料，乘法常数只取决于规定的高斯度量。

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Stability of the Gaussian Faber–Krahn inequality

We prove a quantitative version of the Gaussian Faber–Krahn type inequality proved in (Betta et al. in Z. Angew. Math. Phys. 58:37–52, 2007) for the first Dirichlet eigenvalue of the Ornstein–Uhlenbeck operator, estimating the deficit in terms of the Gaussian Fraenkel asymmetry. As expected, the multiplicative constant only depends on the prescribed Gaussian measure.

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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

期刊介绍： This journal, the oldest scientific periodical in Italy, was originally edited by Barnaba Tortolini and Francesco Brioschi and has appeared since 1850. Nowadays it is managed by a nonprofit organization, the Fondazione Annali di Matematica Pura ed Applicata, c.o. Dipartimento di Matematica "U. Dini", viale Morgagni 67A, 50134 Firenze, Italy, e-mail annali@math.unifi.it). A board of Italian university professors governs the Fondazione and appoints the editors of the journal, whose responsibility it is to supervise the refereeing process. The names of governors and editors appear on the front page of each issue. Their addresses appear in the title pages of each issue.