Finite Propagation Speed for Solutions of the Parabolic p-Laplace Equation on Manifolds
Finite Propagation Speed for Solutions of the Parabolic p-Laplace Equation on Manifolds
复制标题
流形上抛物型p-拉普拉斯方程解的有限传播速度
DOI：
10.4310/cag.2005.v13.n4.a5
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发表时间：
2005
影响因子：
0.7
通讯作者：
S. Dekkers
中科院分区：
文献类型：
--
作者：
S. Dekkers
考虑黎曼流形上一类包含抛物p-Laplace方程的退化抛物方程。我们证明了，在任意流形上，有界的解决方案，这样的方程有有限的传播速度，并表明，传播速度可以估计的Ricci曲率的界限。证明的主要技术工具是一个新的有界解的均值型不等式。
We consider a class of degenerate parabolic equations containing the parabolic p-Laplace equation, on Riemannian manifolds. We prove that, on arbitrary manifolds, bounded solutions of such equations have finite propagation speed, and show that the rate of propagation can be estimated in terms of bounds on the Ricci curvature. The main technical tool in the proof is a new mean value type inequality for bounded solutions.