论文标题
在非线性操作员的主要特征值的下限
On the Lower Bound of the Principal Eigenvalue of a Nonlinear Operator
论文作者
论文摘要
我们证明，在平滑的度量度量空间上，非线性椭圆扩散算子$ L_P $的第一个非零特征值的急剧下限估计值，没有边界或具有凸边界和Neumann边界条件，满足$（κ，n）$的$κ\ neq 0 $。我们的结果扩展了Koerber [5]的案例$κ= 0 $和Naber-Valtorta [10]的工作。
We prove sharp lower bound estimates for the first nonzero eigenvalue of the non-linear elliptic diffusion operator $L_p$ on a smooth metric measure space, without boundary or with a convex boundary and Neumann boundary condition, satisfying $BE(κ,N)$ for $κ\neq 0$. Our results extends the work of Koerber[5] for case $κ=0$ and Naber-Valtorta[10] for the $p$-Laplacian.
