带权散度型椭圆算子的低阶特征值估计

Estimates for the Lower Order Eigenvalues of Elliptic Operators in Weighted Divergence Form

中文关键词:  万有不等式  drifting拉普拉斯算子  带权散度型算子  光滑度量测度空间

英文关键词:universal inequalities  drifting Laplacian  elliptic operators in weighted divergence form  smooth metric measure space

中文摘要:

      本文首先给出紧致带边(边界可以为空集)光滑度量测度空间上带权散度型算子的低阶特征值的一个一般不等式,通过使用这个一般不等式,可以得到光滑度量测度空间中有界连通区域上带权散度型算子的低阶特征值的一些万有不等式.

英文摘要:

      In this paper, we firstly give a general inequality for the lower order eigenvalues of elliptic operators in weighted divergence form on compact smooth metric measure spaces with boundary (possibly empty). Then using this general inequality, we get some universal inequalities for the lower order eigenvalues of elliptic operators in weighted divergence form on a connected bounded domain in the smooth metric measure spaces.