Jie He

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math.AP2025

Optimal Liouville theorems for the Lane-Emden equation on Riemannian manifolds

Jie He, Linlin Sun, Youde Wang

We study degenerate quasilinear elliptic equations on Riemannian manifolds and obtain several Liouville theorems. Notably, we provide rigorous proof asserting the nonexistence of p…

math.AP2024

Local and Global Log-Gradient estimates of solutions to $I^_{p} v + b v^{q} + c v^{r} = 0$ on manifolds and applications

Jie He, Yuanqing Ma, Youde Wang

In this paper, we employ the Nash-Moser iteration technique to study local and global properties of positive solutions to the equation $I^_{p} v + b v^{q} + c v^{r} = 0$ on complete Riemannian…

Optimal Liouville theorems for the Lane-Emden equation on Riemannian manifolds

Local and Global Log-Gradient estimates of solutions to I^p​v+bvq+cvr=0 on manifolds and applications

Local and Global Log-Gradient estimates of solutions to $I^_{p} v + b v^{q} + c v^{r} = 0$ on manifolds and applications