3 research outputs found
Elliptic gradient estimates and Liouville theorems for a weighted nonlinear parabolic equation
Let be a complete smooth metric measure space with
-Bakry-\'Emery Ricci tensor bounded from below. We derive elliptic
gradient estimates for positive solutions of a weighted nonlinear parabolic
equation \begin{align*} \displaystyle \Big(\Delta_f - \frac{\partial}{\partial
t}\Big) u(x,t) +q(x,t)u^\alpha(x,t) = 0, \end{align*} where and is an arbitrary constant. As
Applications we prove a Liouville-type theorem for positive ancient solutions
and Harnack-type inequalities for positive bounded solutions.Comment: 18 page