Gradient estimates for nonlinear elliptic equations involving the Witten Laplacian on smooth metric measure spaces and implications
Gradient estimates for nonlinear elliptic equations involving the Witten Laplacian on smooth metric measure spaces and implications
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DOI：
10.1515/anona-2022-0288
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发表时间：
2023-01
影响因子：
4.2
通讯作者：
A. Taheri;Vahideh Vahidifar
中科院分区：
文献类型：
--
作者：
A. Taheri;Vahideh Vahidifar
摘要本文给出了光滑度量测度空间上一类含维滕拉普拉斯算子的非线性椭圆型方程正解的Li-Yau型局部和整体梯度估计.这些估计是在相关的Bakry-Émery Ricci曲率张量的自然下界下得出的，并且在证明相当一般的Harnack不等式和Liouville型定理中找到了实用性。这里的结果统一，扩展和改善各种现有的结果在文献中的特殊非线性已经有巨大的兴趣和应用。一些后果进行了介绍和讨论。
Abstract This article presents new local and global gradient estimates of Li-Yau type for positive solutions to a class of nonlinear elliptic equations on smooth metric measure spaces involving the Witten Laplacian. The estimates are derived under natural lower bounds on the associated Bakry-Émery Ricci curvature tensor and find utility in proving fairly general Harnack inequalities and Liouville-type theorems to name a few. The results here unify, extend and improve various existing results in the literature for special nonlinearities already of huge interest and applications. Some consequences are presented and discussed.