In this paper we study an optimal control problem for a linear boundary value problem with strongly degenerate coefficient in the main part of the elliptic operator and with the Neumann boundary control. Given a cost functional, the objective is to provide the well-posedness analysis of the corresponding optimal control problem, prove existence of the optimal solutions and propose the scheme for their approximation.

中文翻译：

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强退化椭圆方程的最优边界控制问题

在本文中，我们研究了在椭圆算子的主体中具有严重退化系数的线性边值问题和诺伊曼边界控制的最优控制问题。给定成本函数，目标是提供相应最优控制问题的适定性分析，证明最优解的存在并提出近似方案。