Weak Monotonicity for Weak Solutions to Elliptic Equations with Degenerate Coercivity

GAO Hongya, LIANG Shuang adn C

Abstract

Weak monotonicity result is obtained for weak solutions to elliptic equations of the type −div(a(x, u)|Du| p−2Du) = 0, x ∈ Ω, p > 1, where a(x, s) : Ω × R → R satisfies α (1 + |s|) θ ≤ a(x, s) ≤ β, α ≤ β < ∞, 0 < θ < 1.