Reilly-type inequalities for <i>p</i>-Laplacian on compact Riemannian manifolds

doi:10.1007/s11464-015-0422-x

Front. Math. China

2015, Vol. 10

Issue (3) : 583-594 https://doi.org/10.1007/s11464-015-0422-x

RESEARCH ARTICLE

Reilly-type inequalities for p-Laplacian on compact Riemannian manifolds

Feng DU¹,Jing MAO^2,^*(

)

1. School of Mathematics and Physics Science, Jingchu University of Technology, Jingmen 448000, China
2. Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai 264209, China

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Abstract

For a compact Riemannian manifold M immersed into a higher dimensional manifold which can be chosen to be a Euclidean space, a unit sphere, or even a projective space, we successfully give several upper bounds in terms of the norm of the mean curvature vector of M for the first non-zero eigenvalue of the p-Laplacian (1<p<+∞) on M. This result can be seen as an extension of Reilly’s bound for the first non-zero closed eigenvalue of the Laplace operator.

Keywords p-Laplacian eigenvalue mean curvature vector

Corresponding Author(s): Jing MAO

Issue Date: 01 April 2015

Cite this article:

Feng DU,Jing MAO. Reilly-type inequalities for p-Laplacian on compact Riemannian manifolds[J]. Front. Math. China, 2015, 10(3): 583-594.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-015-0422-x
https://academic.hep.com.cn/fmc/EN/Y2015/V10/I3/583

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