# PDE Seminar

## A priori estimates for elliptic equations with a source term involving the product of the function and its gradient

### Prof. Marie Francoise BIDAUT-VERON (Universite de Tours, France)

#### 2018年6月28日下午3:30-4:30 闵行校区行政楼12楼PDE中心1202报告厅

Abstract: Here we consider the nonnegative solutions of equations in a punctured ball $B(0,R)\backslash\left\{ 0\right\} \subset\mathbb{R}^{N}$ or in $\mathbb{R}^{N},$ of the type \[ -\Delta u=u^{p}|\nabla u|^{q}% \] where $p+q>1.$ We give new a priori estimates on the solutions and their gradient, and Liouville type results, extending the case $q=0$ of the well known Emden-Fowler equation. We use Bernstein technique and Osserman's or Gidas-Spruck's type methods.