Harnack inequality for quasilinear elliptic equations with (p,q) growth conditions and absorption lower order term
Date
2018-04-16
Authors
Buryachenko, Kateryna
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article we study the quasilinear elliptic equation with absorption lower term
-div (g(|∇u|) ∇u/|∇u|) + ƒ(u) = 0, u ≥ 0.
Despite of the lack of comparison principle, we prove a priori estimate of Keller-Osserman type. Particularly, under some natural assumptions on the functions g, ƒ for nonnegative solutions we prove an estimate of the form
∫0u(x) ƒ(s) ds ≤ c u(x)/r g(u(x)/r), x ∈ Ω, B8r(x) ⊂ Ω,
with constant c, independent on u(x). Using this estimate we give a simple proof of the Harnack inequality.
Description
Keywords
Harnack inequality, Quasilinear elliptic equation, Keller-Osserman type estimate, Absorption lower term
Citation
Buryachenko, K. (2018). Harnack inequality for quasilinear elliptic equations with (p,q) growth conditions and absorption lower order term. Electronic Journal of Differential Equations, 2018(91), pp. 1-9.
Rights
Attribution 4.0 International