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

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2024年9月12日

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Roberta Filippucci,
Yuhua Sun,
Yadong Zheng

摘要

In this article we study local and global properties of positive solutions of − Δ_mu = ∣u∣^p−1u+M∣∇u∣^q in a domain Ω of ℝ^N, with m > 1, p, q > 0 and M ∈ ℝ. Following some ideas used in [7, 8], 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.