加权拉普拉斯算子和加权p -拉普拉斯算子的特征值估计

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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