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

Sharp lower bounds for the first eigenvalues of the bi-drifting Laplacian

“…where ∇ and △ are the gradient operator and the Laplace operator, respectively. Some interesting results concerning eigenvalues of the drifting Laplacian can be found, for instance, in [10,13,19,27,37], among others. On smooth metric measure spaces, we can also define the so-called Bakry-Emery Ricci tensor Ric φ by…”

The eigenvalues inequalities of the weighted Paneitz operator and weighted vibration problem for a clamped plate

“…事实上, 我们得到下面的定理: [9] 给出了 (1.6) 的 特征值的一些等周不等式, 而 Xia [10] 则给出了 (1.6) 的特征值的万有不等式. 当 τ = 0 时, 相关的特 征值估计结果可参见文献 [11][12][13][14].…”

Estimates for eigenvalues of weighted Laplacian and weighted $p$-Laplacian

“…Clearly, the first eigenvalue l 0 has multiplicity one and constant eigenfunction. In recent years, there are some interesting results concerning eigenvalue estimates of the drifting Laplacian and the bi-drifting Laplacian-see, e.g., [9,11,12,15,18,21,22,23,30]. When ðM; h ; iÞ is immersed into the Euclidean N-space ðR N ; canÞ with the canonical metric can, one can define the weighted mean curvature vector as ? , where H is the mean curvature vector of M in R N , ð'f Þ ?…”