Optimization problems and mathematical analysis of optimal values in Orlicz spaces

Abstract

This article concerns a minimization problem related to an elliptic equation in Orlicz-Sobolev spaces. We prove existence and uniqueness of optimal solutions and show that they are monotone and stable. Furthermore, by employing a characterization of the tangent cones in L∞ spaces, we derive some qualitative properties of the optimal solutions. We also derive some results regarding the optimal values.