Open AccessGradient estimates for bounded solutions of semilinear elliptic equations and the Allen-Cahn equation on manifolds
Author(s) -
Abimbola Abolarinwa,
S.O. Edeki,
N. K. Oladejo,
O. P. Ogundile
Publication year - 2022
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/2199/1/012002
Subject(s) - bounded function , mathematics , allen–cahn equation , ricci curvature , riemannian manifold , mathematical analysis , manifold (fluid mechanics) , a priori and a posteriori , curvature , elliptic curve , pure mathematics , geometry , mechanical engineering , philosophy , epistemology , engineering
This paper aims at deriving apriori bounds on the gradient of positve solutions to a class of semilinear elliptic equation, with applications focusing on establishing a liouville type property for the bounded solutions of the Allen-Cahn equation on a complete noncompact Riemannian manifold with nonnegative Ricci curvature.