黎曼流形上关于p-Laplace热方程的Harnack不等式

A Harnack Inequlity for p-Laplace Heat Equation on Riemannian Manifolds

本文主要讨论Ｒｉｅｍａｎｎ流形上型如：ｄｉｖ（ｕ~ｐ－２ｕ）－ｕ~ｐ－２ｕ－２ｔ＝０（ｐ＞１）的非线性抛物方程（ｐ＞１），导出其正解的局部Ｈａｒｎａｃｋ不等式，推广了文献［１，２］中的结果．

In this paper, we will consider the non-linear parabolic equation: div (u^p-2 u) -u^p-2u = 0, for p > 1, on complete Riemannian manifolds. We derive a locally Harnack inequality for positive solution of this equation, then we generalize the results in [1, 2].