Gradient Estimations for Nonlinear Elliptic Equations on Weighted Riemannian Manifolds

被引：1

作者：

Hui, Shyamal Kumar ^{[1
]}

Abolarinwa, Abimbola ^{[2
]}

Bhattacharyya, Sujit ^{[1
]}

机构：

[1] Univ Burdwan, Dept Math, Burdwan 713104, W Bengal, India

[2] Univ Lagos, Dept Math, Akoka, Lagos State, Nigeria

来源：

LOBACHEVSKII JOURNAL OF MATHEMATICS | 2023年 / 44卷 / 04期

关键词：

gradient estimate; weighted Laplacian; elliptic equation; Liouville theorem;

D O I：

10.1134/S1995080223040121

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, we derive local gradient estimates for positive solutions of a generalized nonlinear weighted elliptic equation Delta(phi)u + au(p)(ln u)(q) + bu(r) = 0, where a, b, p, q, r are real constants, under the lower bound assumption on Bakry-E ' mery Ricci tensor on a complete weighted Riemannian manifold without imposing bounds on |del phi|. As applications we provide global gradient estimate for the same equation and establish Liouville type theorems.

引用

页码：1341 / 1349

页数：9

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