Estimates for eigenvalues of a system of elliptic equations with drift and of bi-drifting laplacian
Estimates for eigenvalues of a system of elliptic equations with drift and of bi-drifting laplacian
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DOI：
10.3934/cpaa.2017024
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发表时间：
2016
影响因子：
1
通讯作者：
Feng Du;A. C. Bezerra
中科院分区：
文献类型：
--
作者：
Feng Du;A. C. Bezerra
本文首先研究了带漂移的椭圆方程组的特征值问题，得到了欧几里德空间和高斯收缩孤子有界域上PayneP'olya-Weinberger-Yang型的普适不等式。此外，我们研究了两类双向漂移拉普拉斯的夹板问题和屈曲问题，并得到了这些具有边界和正m加权Ricci曲率的紧流形上或在加权Ricci曲率上某种条件下具有边界的紧流形上这些特征值问题的第一特征值的尖锐下界。
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.