Title of article
A Gradient Bound for the Allen-Cahn Equation Under Almost Ricci Solitons
Author/Authors
Hajiaghasi ، Sakineh Department of Pure Mathematics - Faculty of Science - Imam Khomeini International University , Azami ، Shahroud Department of Pure Mathematics - Faculty of Science - Imam Khomeini International University
From page
83
To page
98
Abstract
In this paper, we consider positive solutions for the Allen-Cahn equation ∆u +(1 − u2) u=0, on an almost Ricci soliton without a boundary. Firstly, using vol-ume comparison Theorem and Sobolev inequality, we estimate the upper bound of |∇u|2. As one of the applications, we extend this result to a gradient Ricci almost soliton. Finally, we obtain a Liouville-type theorem for almost Ricci solitons.
Keywords
Gradient estimate , Almost Ricci soliton , Allen , Cahn equation
Journal title
Sahand Communications in Mathematical Analysis
Journal title
Sahand Communications in Mathematical Analysis
Record number
2754329
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