Optimal rearrangement problem and normalized obstacle problem in the fractional setting

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Bonder, Julián Fernández, 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: https://eprints.nottingham.ac.uk/id/eprint/60945

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