Lower bound estimates for the first eigenvalue of the weighted p-Laplacian on smooth metric measure spaces
Lower bound estimates for the first eigenvalue of the weighted p-Laplacian on smooth metric measure spaces
复制标题
平滑度量测度空间上加权 p-拉普拉斯算子的第一个特征值的下界估计
DOI：
10.1016/j.difgeo.2015.11.008
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发表时间：
2016
影响因子：
0.5
通讯作者：
Li Huaiqian
中科院分区：
文献类型：
--
作者：
Wang Yuzhao;Li Huaiqian
加权 p-拉普拉斯算子的第一个非零特征值的新下界建立在有边界或无边界的紧致光滑度量测度空间上。在 m-Bakry-Émery Ricci 曲率的正下界假设下，证明了 Escobar-Lichnerowicz-Reilly 型估计；在非负 ∞-Bakry-Émery Ricci 曲率和 m-Bakry-Émery Ricci 曲率从下界受非正常数限制的假设下，给出了 Li-Yau 型下界估计。推导了加权p-Bochner公式和加权p-Reilly公式作为建立上述结果的关键工具。
New lower bounds of the first nonzero eigenvalue of the weighted p-Laplacian are.established on compact smooth metric measure spaces with or without boundaries..Under the assumption of positive lower bound for the m-Bakry–Émery Ricci.curvature, the Escobar–Lichnerowicz–Reilly type estimates are proved; under the.assumption of nonnegative ∞-Bakry–Émery Ricci curvature and the m-Bakry–.Émery Ricci curvature bounded from below by a non-positive constant, the Li–Yau.type lower bound estimates are given. The weighted p-Bochner formula and the.weighted p-Reilly formula are derived as the key tools for the establishment of the.above results.