Electronic Journal of Differential Equations, 
Vol. 2021 (2021), No. 38, pp. 1-14.

Title: Optimization problems and mathematical analysis of optimal values in Orlicz spaces
       
Authors: Zahra Donyari (Shahid Chamran Univ., Ahvaz, Iran)
         Mohsen Zivari-Rezapour (Shahid Chamran Univ., Ahvaz, Iran)
         Behrouz Emamizadeh (Univ. of Nottingham Ningbo, Ningbo, China)

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 $L^\infty$ spaces, we  derive some qualitative properties
 of the optimal solutions. We also derive some results regarding the optimal values.

Submitted April 12, 2021. Published May 06, 2021.
Math Subject Classifications: 35J25, 49K20.
Key Words: Existence; uniqueness; Orlicz spaces; minimization; tangent cone;
           optimal solutions; optimal values.