Estimates for eigenvalues of a system of elliptic equations with drift and of bi-drifting laplacian

Feng Du; Adriano Cavalcante Bezerra

doi:10.3934/cpaa.2017024

Article Contents

2017, Volume 6: 475-491. Doi: 10.3934/cpaa.2017024

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Estimates for eigenvalues of a system of elliptic equations with drift and of bi-drifting laplacian

Feng Du^1,2 and
Adriano Cavalcante Bezerra²

1.
School of Mathematics and Physics Science, Jingchu University of Technology, Jingmen, 448000, China
2.
Departamento de Matemática, Universidade de Brasilia, 70910-900-Brasilia-DF, Brazil

Received: April 2016

Revised: October 2016

Published: February 2017

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Abstract

In this paper, we firstly study the eigenvalue problem of a systemof elliptic equations with drift and get some universal inequalities of PayneP′olya-Weinberger-Yang type on a bounded domain in Euclidean spaces and inGaussian shrinking solitons. Furthermore, we study two kinds of the clampedplate problems and the buckling problems for the bi-drifting Laplacian and getsome sharp lower bounds for the first eigenvalue for these eigenvalue problemon compact manifolds with boundary and positive m-weighted Ricci curvatureor on compact manifolds with boundary under some condition on the weightedRicci curvature.

Keywords:

Eigenvalue,
universal inequalities,
system of elliptic equations with drift,
drifting Laplacian,
$m$-weighted Ricci curvature,
Gaussian shrinking soliton.

Mathematics Subject Classification: 35P15, 53C20, 53C42.

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References

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