The first eigenfunctions and eigenvalue of the p-Laplacian on Finsler manifolds

被引：5

作者：

Yin SongTing ^{[1
]}

He Qun ^{[2
]}

机构：

[1] Tongling Univ, Dept Math & Comp Sci, Tongling 244000, Peoples R China

[2] Tongji Univ, Sch Math Sci, Shanghai 200092, Peoples R China

来源：

SCIENCE CHINA-MATHEMATICS | 2016年 / 59卷 / 09期

基金：

中国国家自然科学基金;

关键词：

the first eigenvalue; p-Laplacian; Ricci curvature; S curvature; COMPACT RIEMANNIAN MANIFOLD; ELLIPTIC-EQUATIONS; RICCI CURVATURE; LOWER BOUNDS; INEQUALITIES; REGULARITY; FORMULA;

D O I：

10.1007/s11425-015-0411-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper proves that the first eigenfunctions of the Finsler p-Lapalcian are C-1,C- alpha. Using a gradient comparison theorem and one-dimensional model, we obtain the sharp lower bound of the first Neumann and closed eigenvalue of the p-Laplacian on a compact Finsler manifold with nonnegative weighted Ricci curvature, on which a lower bound of the first Dirichlet eigenvalue of the p-Laplacian is also obtained.

引用

页码：1769 / 1794

页数：26

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