Gradient estimates for bounded solutions of semilinear elliptic equations and the Allen-Cahn equation on manifolds
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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.
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QA Mathematics