The asymptotic behavior of solutions to a class of inhomogeneous problems: an Orlicz–Sobolev space approach

Abstract

The asymptotic behavior of the sequence $\{v_n\}$ of nonnegative solutions for a class of inhomogeneous problems settled in Orlicz–Sobolev spaces with prescribed Dirichlet data on the boundary of domain $\Omega$ is analysed. We show that $\{v_n\}$ converges uniformly in $\Omega$ as $n\rightarrow\infty$, to the distance function to the boundary of the domain.

Keywords

• weak solution
• viscosity solution
• nonlinear elliptic equations
• asymptotic behavior
• orlicz–sobolev spaces