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math.AP2026
Logarithmic gradient estimate and Universal bounds for semilinear elliptic equations revisited
Zhihao Lu
We derive the complete and optimal Cheng--Yau gradient estimates and universal bounds for subcritical semilinear elliptic equations on Riemannian manifolds with (Bakry-Ãmery) Ricc…
math.AP2024
Liouville theorems and Harnack inequalities for Allen-Cahn type equation
Zhihao Lu
We first give a logarithmic gradient estimate for positive solutions of Allen-Cahn equation on Riemannian manifolds with Ricci curvature bounded below. As its natural corallary, Ha…
math.AP2024
Differential Harnack inequalities for Fisher-KPP type equations on Riemannian manifolds
Zhihao Lu
We obtain almost optimal differential Harnack inequalities for a class of nonlinear parabolic equations on Riemannian manifolds with Bakry-Ãmery Ricci curvature bounded below, whi…