## View abstract

### Session S38 - Geometric Potential Analysis

Monday, July 19, 19:35 ~ 20:05 UTC-3

## A Sharp Liouville Principle for $\Delta_m u+u^p|\nabla u|^q\leq 0$ on Geodesically Complete Noncompact Riemannian Manifolds

### Yuhua Sun

For $(m,p,q)\in (1,\infty)\times\mathbb R\times\mathbb R$, this paper establishes a sharp Liouville principle for the weak solutions to the quasilinear elliptic inequality of second order $\Delta_m u+u^p|\nabla u|^q\leq0$ on the geodesically complete noncompact Riemannian manifolds, which is novel even in the special case of Euclidean space.