Frontiers of Mathematics in China >
Reilly-type inequalities for p-Laplacian on compact Riemannian manifolds
Received date: 14 Nov 2013
Accepted date: 22 Jul 2014
Published date: 01 Apr 2015
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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.
Key words: p-Laplacian; eigenvalue; mean curvature vector
Feng DU , Jing MAO . Reilly-type inequalities for p-Laplacian on compact Riemannian manifolds[J]. Frontiers of Mathematics in China, 2015 , 10(3) : 583 -594 . DOI: 10.1007/s11464-015-0422-x
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