Convexity of the first eigenfunction of the drifting Laplacian operator and its applications
Convexity of the first eigenfunction of the drifting Laplacian operator and its applications
复制标题
DOI：
--
复制
发表时间：
2008
期刊：
影响因子：
--
通讯作者：
Li Ma;Baiyu Liu
中科院分区：
文献类型：
--
作者：
Li Ma;Baiyu Liu
本文证明了Dirichlet边值为零的漂移Laplacian算子的第一本征函数的凸性，并对漂移项作了适当的假设。在给出梯度估计后，利用第一特征函数的凸性得到漂移拉普拉斯算子的第一、第二特征值之差的下界。
In this short note, we prove the convexity of the first eigen- function of the drifting Laplacian operator with zero Dirichlet boundary value provided a suitable assumption to the drifting term is added. After giving a gradient estimate, we then use the convexity of the first eigen- function to get a lower bound of the difference of the first and second eigenvalues of the drifting Laplacian.