保角 CR 子拉普拉斯障碍问题的优化控制

Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-03-04 DOI:10.1007/s00030-024-00923-w

Pak Tung Ho, Cheikh Birahim Ndiaye

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引用次数: 0

摘要

本文研究了紧凑伪全息流形上与共形CR子拉普拉奇障碍问题相关的最优控制问题。当 CR Yamabe 常数为正数时，我们证明了最优控制等于其相关的最优状态，并证明了一个平滑最优控制的存在，它诱导了一个具有恒定韦伯斯特标量曲率的共形接触形式。

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Optimal control for the conformal CR sub-Laplacian obstacle problem

In this paper, we study an optimal control problem associated to the conformal CR sub-Laplacian obstacle problem on a compact pseudohermitian manifold. When the CR Yamabe constant is positive, we show that the optimal controls are equal to their associated optimal states and show the existence of a smooth optimal control which induces a conformal contact form with constant Webster scalar curvature.

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Nonlinear Differential Equations and Applications (NoDEA)

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