论文标题
laplacian特征值之间的一些不平等现象
Some inequalities between Laplacian eigenvalues on Riemannian manifolds
论文作者
论文摘要
在本文中，我们研究了一个完整加权的riemannian歧管中有界域上加权$ p $ laplacian的第一个dirichlet本征函数。通过为第一个本征函数构建梯度估计，我们获得了加权$ p $ laplacian第一特征值之间的一些关系。作为立即应用，我们还获得了加权拉普拉斯的第一个迪里奇特征值，第一个夹紧板特征值和第一个屈曲特征值之间的特征值比较结果。
In this paper, we study a first Dirichlet eigenfunction of the weighted $p$-Laplacian on a bounded domain in a complete weighted Riemannian manifold. By constructing gradient estimates for a first eigenfunction, we obtain some relationships between weighted $p$-Laplacian first eigenvalues. As an immediate application, we also obtain some eigenvalue comparison results between the first Dirichlet eigenvalue of the weighted Laplacian, the first clamped plate eigenvalue and the first buckling eigenvalue.
