Gradient estimates and Harnack inequalities for diffusion equation on Riemannian manifolds

Yue Wang

doi:10.1007/s11464-010-0080-y

Front. Math. China ›› 2010, Vol. 5 ›› Issue (4) : 727 -746. DOI: 10.1007/s11464-010-0080-y

Research Article

RESEARCH ARTICLE

Gradient estimates and Harnack inequalities for diffusion equation on Riemannian manifolds

Yue Wang ¹^,^a

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Abstract

We derive the gradient estimates and Harnack inequalities for positive solutions of the diffusion equation u_t = Δu^m on Riemannian manifolds. Then, we prove a Liouville type theorem.

Keywords

Gradient estimate / Harnack inequality / diffusion equation / Riemannian manifold

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Yue Wang. Gradient estimates and Harnack inequalities for diffusion equation on Riemannian manifolds. Front. Math. China, 2010, 5(4): 727-746 DOI:10.1007/s11464-010-0080-y

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