Gradient estimates for the \(p\)-Laplace heat equation under the Ricci flow. (English) Zbl 1277.53037
The paper establishes “space-only gradient estimates for positive continuous weak solutions to the \(p\)-Laplace heat equation on some complete manifolds evolving under the Ricci flow.” These are first established on compact and then on unbounded complete manifolds. Subsequently, the author proves Harnack inequalities that allow to compare solutions at different points.
Reviewer: Carla Cederbaum (Tübingen)
MSC:
53C21 | Methods of global Riemannian geometry, including PDE methods; curvature restrictions |
35B09 | Positive solutions to PDEs |
35B45 | A priori estimates in context of PDEs |
35D30 | Weak solutions to PDEs |
35K08 | Heat kernel |
35K40 | Second-order parabolic systems |
53C44 | Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010) |