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arXiv · 2205.07484

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

Roberta Filippucci·Yuhua Sun·Yadong Zheng
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Abstract

In this article we study local and global properties of positive solutions of $-\Delta_mu=|u|^{p-1}u+M|\nabla u|^q$ in a domain $\Omega$ 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.

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Roberta Filippucci, Yuhua Sun, Yadong Zheng. 2022-05-16. A priori estimates and Liouville type results for quasilinear elliptic equations involving gradient terms. https://arxiv.org/abs/2205.07484

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