论文标题
帕尼兹障碍问题的最佳控制
Optimal control for the Paneitz obstacle problem
论文作者
论文摘要
在本文中，我们研究了与封闭的4维里工歧管上的帕尼茨障碍问题有关的自然最佳控制问题。我们展示了最佳控制的存在，该控制是最佳状态，并引起了具有规定的Q曲面的共形度量。我们还显示了最佳控件的c^{\ infty} - 最佳控件的一些紧凑性结果。在4维标准球体的情况下，我们表征了所有最佳控件。
In this paper, we study a natural optimal control problem associated to the Paneitz obstacle problem on closed 4-dimensional Riemannian manifolds. We show the existence of an optimal control which is an optimal state and induces also a conformal metric with prescribed Q-curvature. We show also C^{\infty}-regularity of optimal controls and some compactness results for the optimal controls. In the case of the 4-dimensional standard sphere, we characterize all optimal controls.
