HAMILTON'S GRADIENT ESTIMATES AND LIOUVILLE THEOREMS FOR FAST DIFFUSION EQUATIONS ON NONCOMPACT RIEMANNIAN MANIFOLDS

摘要

Let M be a complete noncompact Riemannian manifold of dimension n. In this paper, we derive a local gradient estimate for positive solutions of fast diffusion equations φtu =Δ_u~α,1-1/2 <α < 1 on M × ( -∞ , 0]. We also obtain a theorem of Liouville type for positive solutions of the fast diffusion equation.