The asymptotic behavior of a class of φ-harmonic functions in Orlicz–Sobolev spaces

Abstract

The asymptotic behavior of the sequence {un} of solutions for a class of inhomogeneous problems with prescribed Dirichlet data on the boundary is studied in the setting of Orlicz–Sobolev spaces. We prove that un→u∞ uniformly in Ω as n→∞, where u∞ is an ∞-harmonic function satisfying the prescribed Dirichlet data on the boundary.