5 papers
Inner regularity and Liouville theorems for stable solutions to the mean curvature equation
Fanheng Xu
Let . We study stable solutions of the mean curvature equation \[ \operatorname{div}\left( \frac{\nabla u}{\sqrt{1+|\nabla u|^2}} \right) = -f(u) \qquad \…
Improved Interior Gradient Estimates for the Mean Curvature Equation under Nonlinear Assumptions
Fanheng Xu
In this paper, we investigate interior gradient estimates for solutions to the mean curvature equation $$ \dive \left( \frac{\nabla u}{\sqrt{1 + |\nabla u|^2}} \right) = f(\nabla u…
Liouville's theorems to quasilinear differential inequalities involving gradient nonlinearity term on manifolds
Yuhua Sun, Fanheng Xu
We investigate the nonexistence and existence of nontrivial positive solutions to on noncompact geodesically complete Riemannian manifolds, where …
On nonexistence and existence of positive global solutions to heat equation with a potential term on Riemannian manifolds
Qingsong Gu, Yuhua Sun, Fanheng Xu
We reinvestigate nonexistence and existence of global positive solutions to heat equation with a potential term on Riemannian manifolds. Especially, we give a very natural sharp co…
On existence and nonexistence of nonnegative solutions to seminlinear differential equation on Riemannian manifolds
Fanheng Xu
In this paper, we give a clear cut relation between the the volume growth and the existence of nonnegative solutions to parabolic semilinear problem \begin{align}\tag{*}\lab…