Volume 29, 2023
|Number of page(s)||24|
|Published online||09 June 2023|
Optimal control for the Paneitz obstacle problem
Department of Mathematics Howard University Annex 3, Graduate School of Arts and Sciences 217,
** Corresponding author: email@example.com
Accepted: 1 May 2023
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.
Mathematics Subject Classification: 53C21 / 35C60 / 58J60 / 55N10
Key words: Paneitz operator / Q-curvature / obstacle problem / optimal control
© The authors. Published by EDP Sciences, SMAI 2023
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