1. Gradient estimates on the weighted p-Laplace heat equation.
- Author
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Wang, Lin Feng
- Subjects
- *
HAMILTON-Jacobi equations , *ESTIMATES , *MATHEMATICAL regularization , *HEAT equation , *POTENTIAL functions , *CURVATURE - Abstract
In this paper, by a regularization process we derive new gradient estimates for positive solutions to the weighted p -Laplace heat equation when the m -Bakry–Émery curvature is bounded from below by − K for some constant K ≥ 0 . When the potential function is constant, which reduce to the gradient estimate established by Ni and Kotschwar for positive solutions to the p -Laplace heat equation on closed manifolds with nonnegative Ricci curvature if K ↘ 0 , and reduce to the Davies, Hamilton and Li–Xu's gradient estimates for positive solutions to the heat equation on closed manifolds with Ricci curvature bounded from below if p = 2 . [ABSTRACT FROM AUTHOR]
- Published
- 2018
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