Global Hessian estimates for an Allen-Cahn equation on Riemannian manifolds

In this paper, we establish global bounds for the Hessian of positive smooth solutions to the Allen-Cahn equation of Δu+u(1−u2)=0 on a Riemannian manifold.

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2021-01, Vol.493 (2), p.124573, Article 124573
Main Author: Zhang, Liangdi
Format: Article
Language:English
Subjects:
Allen-Cahn equation
Global Hessian estimate
Riemannian manifold
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Description
Summary:In this paper, we establish global bounds for the Hessian of positive smooth solutions to the Allen-Cahn equation of Δu+u(1−u2)=0 on a Riemannian manifold.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2020.124573