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. <i>Electronic Journal of Differential Equations, 2018</i>(91), pp. 1-9.
Rights
Attribution 4.0 International