{"title":"Paneitz障碍问题的最优控制","authors":"C. B. Ndiaye","doi":"10.1051/cocv/2023036","DOIUrl":null,"url":null,"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.","PeriodicalId":50500,"journal":{"name":"Esaim-Control Optimisation and Calculus of Variations","volume":"9 1","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2022-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Optimal control for the Paneitz obstacle problem\",\"authors\":\"C. B. Ndiaye\",\"doi\":\"10.1051/cocv/2023036\",\"DOIUrl\":null,\"url\":null,\"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.\",\"PeriodicalId\":50500,\"journal\":{\"name\":\"Esaim-Control Optimisation and Calculus of Variations\",\"volume\":\"9 1\",\"pages\":\"\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2022-05-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Esaim-Control Optimisation and Calculus of Variations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1051/cocv/2023036\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"AUTOMATION & CONTROL SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Esaim-Control Optimisation and Calculus of Variations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1051/cocv/2023036","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
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.
期刊介绍:
ESAIM: COCV strives to publish rapidly and efficiently papers and surveys in the areas of Control, Optimisation and Calculus of Variations.
Articles may be theoretical, computational, or both, and they will cover contemporary subjects with impact in forefront technology, biosciences, materials science, computer vision, continuum physics, decision sciences and other allied disciplines.
Targeted topics include:
in control: modeling, controllability, optimal control, stabilization, control design, hybrid control, robustness analysis, numerical and computational methods for control, stochastic or deterministic, continuous or discrete control systems, finite-dimensional or infinite-dimensional control systems, geometric control, quantum control, game theory;
in optimisation: mathematical programming, large scale systems, stochastic optimisation, combinatorial optimisation, shape optimisation, convex or nonsmooth optimisation, inverse problems, interior point methods, duality methods, numerical methods, convergence and complexity, global optimisation, optimisation and dynamical systems, optimal transport, machine learning, image or signal analysis;
in calculus of variations: variational methods for differential equations and Hamiltonian systems, variational inequalities; semicontinuity and convergence, existence and regularity of minimizers and critical points of functionals, relaxation; geometric problems and the use and development of geometric measure theory tools; problems involving randomness; viscosity solutions; numerical methods; homogenization, multiscale and singular perturbation problems.