加权拉普拉斯算子和加权p -拉普拉斯算子的特征值估计

IF 0.5 4区数学 Q3 MATHEMATICS

Hiroshima Mathematical Journal Pub Date : 2021-11-01 DOI:10.32917/h2020086

Feng Du, Jing Mao, Qiaoling Wang, C. Xia

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引用次数: 4

摘要

摘要。本文研究了加权拉普拉斯算子的两个特征值问题，得到了欧氏空间超曲面上第一个非零n个特征值的Reilly型界和等周型界。此外，我们给出了具有局部有界加权平均曲率的子流形上加权p-Laplacian的第一特征值的下界。同时，也给出了这些估计的几种应用。

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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Estimates for eigenvalues of weighted Laplacian and weighted $p$-Laplacian

A bstract . In this paper, we study two eigenvalue problems of the weighted Laplacian and get the Reilly-type bounds and isoperimetric type bounds for the ﬁrst nonzero n eigenvalues on hypersurfaces of the Euclidean space. Besides, we give lower bounds for the ﬁrst eigenvalue of weighted p -Laplacian on submanifolds with locally bounded weighted mean curvature. Meanwhile, several applications of these estimates have also been given.

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来源期刊

Hiroshima Mathematical Journal 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Hiroshima Mathematical Journal (HMJ) is a continuation of Journal of Science of the Hiroshima University, Series A, Vol. 1 - 24 (1930 - 1960), and Journal of Science of the Hiroshima University, Series A - I , Vol. 25 - 34 (1961 - 1970). Starting with Volume 4 (1974), each volume of HMJ consists of three numbers annually. This journal publishes original papers in pure and applied mathematics. HMJ is an (electronically) open access journal from Volume 36, Number 1.