Linear elliptic equations with the coefficients depending on the control function and its gradient are considered, and an optimal control problem for such equations is studied. The existence and uniqueness of the solution of this problem are proved. The results are applied to the optimal control of the boundary of a given domain.

中文翻译：

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椭圆方程系数中带有控制梯度的优化问题

考虑系数取决于控制函数及其梯度的线性椭圆方程，并研究了此类方程的最优控制问题。证明了该问题解的存在性和唯一性。将结果应用于给定域边界的最佳控制。