Optimization problems and mathematical analysis of optimal values in Orlicz spaces

[摘要] This article concerns a minimization problem related to an elliptic equationin Orlicz-Sobolev spaces. We prove existence and uniqueness of optimal solutions andshow that they are monotone and stable. Furthermore, by employing a characterizationof the tangent cones inspaces, we derive some qualitative propertiesof the optimal solutions. We also derive some results regarding the optimal values.

[学科分类] 数学（综合）

[关键词] Existence;uniqueness;Orlicz spaces;minimization;tangent cone;optimal solutions;optimal values.