Strong maximum principle for general quasilinear problems in non-divergence form

Abstract

Let us consider a solution u of the following { − ∑ i j a i j ( x , u , ∇ u ) ∂ 2 u ∂ x i ∂ x j ≥ F ( x , u , ∇ u ) in R N u ( x ) ≥ 0 ∀ x ∈ R N . In this paper we give (i) Some conditions ensuring a strong maximum principle for u . (ii) Some conditions ensuring that u has a compact support.