Gradient estimates and Harnack inequalities for Yamabe-type parabolic equations on Riemannian manifolds

被引：6

作者：

Ha Tuan Dung ^{[1
]}

机构：

[1] Hanoi Pedag Univ, Dept Math, 2 Nguyen Van Linh Rd, Phuc Yen Dist, Vinh Phuc Provi, Vietnam

来源：

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS | 2018年 / 60卷

关键词：

Gradient estimates; Yamabe-type parabolic equations; Harnack inequalities; Liouville-type theorems; Bochner-Weitzenbock; NONCOMPACT MANIFOLDS; SCALAR CURVATURE;

D O I：

10.1016/j.difgeo.2018.05.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let (M-n, g) be a complete noncompact n-dimensional Riemannian manifolds. In this paper, we consider the following Yamabe-type parabolic equation u(t) = Delta u + au + bu(alpha) on M-n x [0, infinity). We give a global gradient estimate of Hamilton-type for positive smooth solutions of this equation provided that Ricci curvature bounded from below. As its application, we show a dimension-free Harnack inequality and a Liouville-type theorem for nonlinear elliptic equations. (C) 2018 Elsevier B.V. All rights reserved.

引用

页码：39 / 48

页数：10

共 50 条

[21] On estimates for augmented Hessian type parabolic equations on Riemannian manifolds
Jiao, Yang
[J]. ELECTRONIC RESEARCH ARCHIVE, 2022, 30 (09): : 3266 - 3289
[22] Differential Harnack inequalities for semilinear parabolic equations on Riemannian manifolds II: Integral curvature condition
Lu, Zhihao
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2024, 239
[23] Gradient estimates and Liouville theorems for nonlinear parabolic equations on noncompact Riemannian manifolds
Zhu, Xiaobao
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (15) : 5141 - 5146
[24] GRADIENT ESTIMATES AND LIOUVILLE THEOREMS FOR LINEAR AND NONLINEAR PARABOLIC EQUATIONS ON RIEMANNIAN MANIFOLDS
朱晓宝
[J]. Acta Mathematica Scientia, 2016, (02) : 514 - 526
[25] Logarithmic Harnack inequalities and differential Harnack estimates for p-Laplacian on Riemannian manifolds
Wang, Yu-Zhao
Xue, Yan
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2023, 523 (02)
[26] GRADIENT ESTIMATES AND LIOUVILLE THEOREMS FOR LINEAR AND NONLINEAR PARABOLIC EQUATIONS ON RIEMANNIAN MANIFOLDS
Zhu, Xiaobao
[J]. ACTA MATHEMATICA SCIENTIA, 2016, 36 (02) : 514 - 526
[27] NODAL SOLUTIONS OF YAMABE-TYPE EQUATIONS ON POSITIVE RICCI CURVATURE MANIFOLDS
Julio-Batalla, Jurgen
Petean, Jimmy
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2021, 149 (10) : 4419 - 4429
[28] Second order estimates for Hessian equations of parabolic type on Riemannian manifolds
Jiao, Heming
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2015, 259 (12) : 7662 - 7680
[29] Yamabe type equations on three dimensional Riemannian manifolds
Li, YY
Zhu, MJ
[J]. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 1999, 1 (01) : 1 - 50
[30] Gradient estimates for a nonlinear parabolic equation on Riemannian manifolds
Huang, Guangyue
Ma, Bingqing
[J]. ARCHIV DER MATHEMATIK, 2010, 94 (03) : 265 - 275

← 1 2 3 4 5 →