Optimal control of nonlinear systems governed by Dirichlet fractional\n Laplacian in the minimax framework

2015/09/03 by Dorota Bors, Bors, Dorota
Computer Science · Mathematics · #35B30 #49J53 #93C10 #93D99 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1509.01283

openalex publication_date 2015/09/03 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28

Abstract

We consider an optimal control problem governed by a class of boundary value\nproblem with the spectral Dirichlet fractional Laplacian. Some sufficient\ncondition for the existence of optimal processes is stated. The proof of the\nmain result relies on variational structure of the problem. To show that\nboundary value problem with the Dirichlet fractional Laplacian has a weak\nsolution we employ the renowned Ky Fan Theorem.\n

Citations

• Hitchhikerʼs guide to the fractional Sobolev spaces
• On the spectrum of two different fractional operators
• Regularity estimates for the solution and the free boundary to the obstacle problem for the fractional Laplacian
• On fractional Poincaré inequalities

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