A class of semilinear elliptic optimal control problems with mixed pointwise constraints is considered. Some criteria under which Lagrange multipliers are functions in $L^p$-spaces are given. Based on the criteria, we establish first- and second-order necessary optimality conditions of KKT-type as well as second-order sufficient optimality conditions for the problem.

中文翻译：

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半线性椭圆控制问题二阶最优条件下乘子的正则性

考虑了一类具有混合逐点约束的半线性椭圆最优控制问题。拉格朗日乘数在其中起作用的一些标准${\mathrm{大号}}^p$-给定空格。基于该准则，我们建立了KKT类型的一阶和二阶必要最优性条件以及问题的二阶充分最优性条件。