Boundary behavior of superharmonic functions satisfying nonlinear inequalities in uniform domains

Abstract

Abstract. In a uniform domain Ω, we investigate the boundary behavior of positive superharmonic functions u satisfying the nonlinear inequalitywith some constants c > 0, α ∈ R and p > 0, where Δ is the Laplacian and δ Ω (x) is the distance from a point x to the boundary of Ω. In particular, we present a Fatou type theorem concerning the existence of nontangential limits and a Littlewood type theorem concerning the nonexistence of tangential limits.