题  目：p-Laplace parabolic equation on manifolds and graphs

报 告 人：王林峰（南通大学）

摘  要： In the first part of this report, by a regularization process we derive a new gradient estimate for the p-Laplace parabolic equation on a closed manifold with the Ricci curvature bounded from below by a negative number, which includes the gradient estimate established by Ni and Kotschwar on closed manifolds with nonnegative Ricci curvature, and also includes the Davies, Hamilton, and Li-Xu's gradient estimates. In the second part of this report, we establish a general gradient estimate for the p-Laplace parabolic equation on a connected finite graph under a suitable curvature-dimension condition. When the curvature is nonnegative we derive the logarithmic gradient estimate; when the curvature is bounded from below by a negative number we derive the Davies, Hamilton, Bakry-Qian and Li-Xu's estimate, as special cases. Based on the gradient estimates, we derive the Harnack inequalities.

时  间:2018年9月28日  10:00—12:00

地  点:蒙民伟楼1105室

邀 请 人：陈学长  老师