Gradient estimates for a nonlinear parabolic equation and Liouville theorems
Differential Geometry
2018-12-04 v3 Analysis of PDEs
Abstract
We establish local elliptic and parabolic gradient estimates for positive smooth solutions to a nonlinear parabolic equation on a smooth metric measure space. As applications, we determine various conditions on the equation's coefficients and the growth of solutions that guarantee the nonexistence of nontrivial positive smooth solutions to many special cases of the nonlinear equation. In particular, we apply gradient estimates to discuss some Yamabe-type problems of complete Riemannian manifolds and smooth metric measure spaces.
Cite
@article{arxiv.1803.10619,
title = {Gradient estimates for a nonlinear parabolic equation and Liouville theorems},
author = {Jia-Yong Wu},
journal= {arXiv preprint arXiv:1803.10619},
year = {2018}
}
Comments
final version, accepted by Manuscripta Math