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

In this paper, we are concerned with Lindelof type theorems for monotone (in the sense of Lebesgue) Sobolev functions u on a uniform domain D subset of Rn satisfying integral(D) vertical bar del u vertical bar(z)(n-1) phi(del u(z)vertical bar)omega(delta(D)(z))dz < infinity where backward difference denotes the gradient, delta D(z) denotes the distance from z to the boundary partial differential D, phi is of log-type and omega is a weight function satisfying the doubling condition.