20220526 孙玉华 A priori estimates and Liouville type results for quasilinear elliptic equations involving gradient terms

【偏微分方程与几何分析学术报告】

报告题目： A priori estimates and Liouville type results for quasilinear elliptic equations involving gradient terms

报告人： 孙玉华 副教授（南开大学）

报告时间：2022/5/26（周四）  10:00-11:00

腾讯会议：663-407-263

邀请人：徐露

报告摘要: In this article, we study local and global properties of positive solutions of $-\Delta_mu=|u|^{p-1}u+M\left|\nabla u\right|^q$ in a domain $\Omega$ of $\mathbb R^N$, with $m>1$, $p,q>0$ and $M\in\mathbb R$. By using a direct Bernstein method combined with Keller-Osserman's estimate, we obtain several a priori estimates as well as Liouville type theorems. Moreover, we prove a local Harnack inequality with the help of Serrin's classical results. This talk is based on joint work with R. Filippucci, and Yadong Zheng.