Gradient estimates for a weighted nonlinear parabolic equation and applications-Reference-Cited by-同舟云学术

Gradient estimates for a weighted nonlinear parabolic equation and applications

Published:2020-01-01 Issue:1 Volume:18 Page:1150-1163
ISSN:2391-5455
Container-title:Open Mathematics
language:en
Short-container-title:

Author:

Abolarinwa Abimbola¹,Oladejo Nathaniel K.¹,Salawu Sulyman O.¹

Affiliation:

1. Department of Mathematics, University of Lagos , Akoka, Lagos State , Nigeria

Abstract

Abstract This paper derives elliptic gradient estimates for positive solutions to a nonlinear parabolic equation defined on a complete weighted Riemannian manifold. Applications of these estimates yield Liouville-type theorem, parabolic Harnack inequalities and bounds on weighted heat kernel on the lower boundedness assumption for Bakry-Émery curvature tensor.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/math-2020-0077/pdf

Reference35 articles.

1. P. Li and S.-T. Yau, On the parabolic kernel of the Schrödinger operator, Acta Math. 156 (1986), 153–201.

2. A. Abolarinwa, Gradient estimates for a nonlinear elliptic equation on complete noncompact Riemannian manifold, J. Math. Ineq. 12 (2018), no. 2, 391–402.

3. A. Abolarinwa, Eigenvalues of weighted-Laplacian under the extended Ricci flow, Adv. Geom. 19 (2019), no. 1, 131–143.

4. A. Abolarinwa and T. Apata, Lp-Hardy-Rellich and uncertainty principle inequalities on the sphere, Adv. Oper. Theory 3 (2018), no. 4, 745–762.

5. A. Abolarinwa, Gradient estimates for a nonlinear parabolic equation with potential under geometric flow, Electr. J. Diff. Eqn. 2015 (2015), no. 12, 1–11.

Cited by 2 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Li–Yau-Type Gradient Estimate along Geometric Flow;Mathematics;2023-03-10

2. Gradient estimates for a weighted nonlinear elliptic equation and Liouville type theorems;Journal of Geometry and Physics;2020-09