Lindelöf theorems for monotone Sobolev functions in Orlicz spaces on uniform domains

In this paper, we are concerned with Lindelöf type theorems for monotone (in the sense of Lebesgue) Sobolev functions u on a uniform domain D ⊂ R nsatisfying∫ D| ∇ u ( z ) | n − 1 φ ( | ∇ u ( z ) | ) ω δ D ( z )d z < ∞ ,where ∇ denotes the gradient,δ D ( z )denotes the distance from z to the boundary ∂ D , φ is of log‐type and ω is a weight function satisfying the doubling condition.