On properties of solutions of quasilinear second-order elliptic inequalities

Abstract

Let Ω be an unbounded open subset of Rn, n≥2, and A:Ω×Rn→Rn be a function such that C1|ζ|p≤ζA(x,ζ),|A(x,ζ)|≤C2|ζ|p−1 with some constants C1>0, C2>0, and p>1 for almost all x∈Ω and for all ζ∈Rn. We obtain blow-up conditions and priori estimates for inequalities of the formdivA(x,Du)+b(x)|Du|α≥q(x)g(u)in Ω, where p−1≤α≤p is a real number and b, q, and g are non-negative functions.