Optimal rearrangement problem and normalized obstacle problem in the fractional setting

Bonder, Julián Fernández and Cheng, Zhiwei and Mikayelyan, Hayk (2020) Optimal rearrangement problem and normalized obstacle problem in the fractional setting. Advances in Nonlinear Analysis, 9 (1). pp. 1592-1606. ISSN 2191-9496

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Abstract

We consider an optimal rearrangement minimization problem involving the fractional Laplace operator (−∆) s , 0 < s < 1, and the Gagliardo seminorm |u|s. We prove the existence of the unique minimizer, analyze its properties as well as derive the non-local and highly non-linear PDE it satis es −(−∆) sU − χ{U≤0} min{−(−∆) sU + ; 1} = χ{U>0} , which happens to be the fractional analogue of the normalized obstacle problem ∆u = χ{u>0} .

Item Type: Article
Keywords: Fractional partial differential equations; Optimization problems; Obstacle problem; 35R11; 35J60
Schools/Departments: University of Nottingham Ningbo China > Faculty of Science and Engineering > School of Mathematical Sciences
Identification Number: https://doi.org/10.1515/anona-2020-0067
Depositing User: Zhou, Elsie
Date Deposited: 22 Jun 2020 02:56
Last Modified: 22 Jun 2020 02:56
URI: http://eprints.nottingham.ac.uk/id/eprint/60945

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