Optimal control for the Paneitz obstacle problem

2022/05/09 by Ndiaye, Cheikh Birahim
#35C60 #53C21 #55N10 #58J60 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2205.04562

Abstract

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^∞-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.

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