Optimal rearrangement problem and normalized obstacle problem in the fractional setting
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...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
2020
|
| Subjects: | |
| Online Access: | https://eprints.nottingham.ac.uk/60945/ |
| _version_ | 1848799824292347904 |
|---|---|
| author | Bonder, Julián Fernández Cheng, Zhiwei Mikayelyan, Hayk |
| author_facet | Bonder, Julián Fernández Cheng, Zhiwei Mikayelyan, Hayk |
| author_sort | Bonder, Julián Fernández |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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} . |
| first_indexed | 2025-11-14T20:41:48Z |
| format | Article |
| id | nottingham-60945 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T20:41:48Z |
| publishDate | 2020 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-609452020-06-22T02:56:32Z https://eprints.nottingham.ac.uk/60945/ Optimal rearrangement problem and normalized obstacle problem in the fractional setting Bonder, Julián Fernández Cheng, Zhiwei Mikayelyan, Hayk 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} . 2020-03-31 Article PeerReviewed application/pdf en cc_by https://eprints.nottingham.ac.uk/60945/1/%5B2191950X%20-%20Advances%20in%20Nonlinear%20Analysis%5D%20Optimal%20rearrangement%20problem%20and%20normalized%20obstacle%20problem%20in%20the%20fractional%20setting.pdf 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 Fractional partial differential equations; Optimization problems; Obstacle problem; 35R11; 35J60 http://dx.doi.org/10.1515/anona-2020-0067 doi:10.1515/anona-2020-0067 doi:10.1515/anona-2020-0067 |
| spellingShingle | Fractional partial differential equations; Optimization problems; Obstacle problem; 35R11; 35J60 Bonder, Julián Fernández Cheng, Zhiwei Mikayelyan, Hayk Optimal rearrangement problem and normalized obstacle problem in the fractional setting |
| title | Optimal rearrangement problem and normalized obstacle problem in the fractional setting |
| title_full | Optimal rearrangement problem and normalized obstacle problem in the fractional setting |
| title_fullStr | Optimal rearrangement problem and normalized obstacle problem in the fractional setting |
| title_full_unstemmed | Optimal rearrangement problem and normalized obstacle problem in the fractional setting |
| title_short | Optimal rearrangement problem and normalized obstacle problem in the fractional setting |
| title_sort | optimal rearrangement problem and normalized obstacle problem in the fractional setting |
| topic | Fractional partial differential equations; Optimization problems; Obstacle problem; 35R11; 35J60 |
| url | https://eprints.nottingham.ac.uk/60945/ https://eprints.nottingham.ac.uk/60945/ https://eprints.nottingham.ac.uk/60945/ |