The Existence and Uniqueness of an Entropy Solution to Unilateral Orlicz Anisotropic Equations in an Unbounded Domain

Abstract

The purpose of this work is to prove the existence and uniqueness of a class of nonlinear unilateral elliptic problem (P) in an arbitrary domain, managed by a low-order term and non-polynomial growth described by an N-uplet of N-function satisfying the Δ2-condition. The source term is merely integrable.

Keywords

• anisotropic elliptic equation
• obstacle problem
• entropy solution
• Sobolev–Orlicz anisotropic spaces
• unbounded domain
• existence and uniqueness