Optimal control for the conformal CR sub-Laplacian obstacle problem

Abstract

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.