Gradient estimates and Liouville type theorems for $$(p-1)^{p-1}\Delta _pu+au^{p-1}\log u^{p-1}=0$$ on Riemannian manifolds

2021 ◽  
Author(s):  
Bingqing Ma ◽  
Mingfang Zhu
Keyword(s):  
Riemannian Manifolds ◽  
Gradient Estimates ◽  
Liouville Type ◽  
Liouville Type Theorems

scholarly journals Hamilton type gradient estimates for a general type of nonlinear parabolic equations on Riemannian manifolds

2021 ◽  
Vol 6 (10) ◽  
pp. 10506-10522
Author(s):  
Fanqi Zeng ◽  
Keyword(s):  
Riemannian Manifolds ◽  
Parabolic Equations ◽  
General Type ◽  
Nonlinear Parabolic Equations ◽  
Complete Riemannian Manifold ◽  
Gradient Estimates ◽  
Geometric Flow ◽  
Liouville Type ◽  
Nonlinear Parabolic ◽  
Liouville Type Theorems

<abstract><p>In this paper, we prove Hamilton type gradient estimates for positive solutions to a general type of nonlinear parabolic equation concerning $ V $-Laplacian:</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ (\Delta_{V}-q(x, t)-\partial_{t})u(x, t) = A(u(x, t)) $\end{document} </tex-math></disp-formula></p> <p>on complete Riemannian manifold (with fixed metric). When $ V = 0 $ and the metric evolves under the geometric flow, we also derive some Hamilton type gradient estimates. Finally, as applications, we obtain some Liouville type theorems of some specific parabolic equations.</p></abstract>

Liouville Type Theorems in the Theory of Mappings of Complete Riemannian Manifolds

2017 ◽  
Vol 221 (6) ◽  
pp. 737-744
Author(s):  
I. A. Aleksandrova ◽  
J. Mikeš ◽  
S. E. Stepanov ◽  
I. I. Tsyganok
Keyword(s):  
Riemannian Manifolds ◽  
Liouville Type ◽  
Liouville Type Theorems ◽  
Complete Riemannian Manifolds
Sign in / Sign up

Export Citation Format

Share Document