一类具有Dirichlet边界条件的非线性抛物方程的梯度估计

IF 0.4 4区 数学 Q4 MATHEMATICS Kodai Mathematical Journal Pub Date : 2021-12-12 DOI:10.2996/kmj/kmj45106
Xu-Yang Fu, Jia-Yong Wu
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引用次数: 7

摘要

. 本文证明了当Bakry-Emery Ricci张量和加权平均曲率均有界时,光滑度量空间上具有紧边界的非线性抛物方程在Dirichlet边界条件下的Souplet-Zhang型梯度估计。作为应用,我们得到了该类光滑度量测度空间上若干时空函数的一个新的Liouville型结果。这些结果将以前的线性方程推广到非线性情况。
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Gradient estimates for a nonlinear parabolic equation with Dirichlet boundary condition
. In this paper, we prove Souplet-Zhang type gradient estimates for a nonlinear parabolic equation on smooth metric measure spaces with the compact boundary under the Dirichlet boundary condition when the Bakry-Emery Ricci tensor and the weighted mean curvature are both bounded below. As an application, we obtain a new Liouville type result for some space-time functions on such smooth metric measure spaces. These results generalize previous linear equations to a nonlinear case.
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来源期刊
CiteScore
0.90
自引率
0.00%
发文量
16
审稿时长
>12 weeks
期刊介绍: Kodai Mathematical Journal is edited by the Department of Mathematics, Tokyo Institute of Technology. The journal was issued from 1949 until 1977 as Kodai Mathematical Seminar Reports, and was renewed in 1978 under the present name. The journal is published three times yearly and includes original papers in mathematics.
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