论文标题
涉及梯度术语的准线性椭圆方程的先验估计和liouville类型结果
A priori estimates and Liouville type results for quasilinear elliptic equations involving gradient terms
论文作者
论文摘要
在本文中，我们研究了$-Δ_MU= | U |^{p-1} u+m | \ nabla u |^q $的本地和全球属性。遵循\ cite {bv，vron1}中使用的一些想法，并使用直接的伯恩斯坦方法与凯勒·塞默曼（Keller-Sosserman）的估计相结合，我们获得了几个先验估计以及liouville型定理。此外，我们在塞林的经典结果的帮助下证明了当地的harnack不平等。
In this article we study local and global properties of positive solutions of $-Δ_mu=|u|^{p-1}u+M|\nabla u|^q$ in a domain $Ω$ of $\mathbb R^N$, with $m>1$, $p,q>0$ and $M\in\mathbb R$. Following some ideas used in \cite{BV,Vron1}, and 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.
