| Issue |
ESAIM: COCV
Volume 29, 2023
|
|
|---|---|---|
| Article Number | 42 | |
| Number of page(s) | 24 | |
| DOI | https://doi.org/10.1051/cocv/2023036 | |
| 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,
Washington,
DC
20059,
USA
** Corresponding author: cheikh.ndiaye@howard.edu
Received:
25
July
2022
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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