Regularity of local minimizers of the interaction energy via obstacle problems
The repulsion strength at the origin for repulsive/attractive potentials determines the regularity of local minimizers of the interaction energy. In this paper, we show that if this repulsion is like Newtonian or more singular than Newtonian (but still locally integrable), then the local minimizers...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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Springer Science and Business Media LLC
2016
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| _version_ | 1797098653112860672 |
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| author | Carrillo de la Plata, JA Delgadino, MG Mellet, A |
| author_facet | Carrillo de la Plata, JA Delgadino, MG Mellet, A |
| author_sort | Carrillo de la Plata, JA |
| collection | OXFORD |
| description | The repulsion strength at the origin for repulsive/attractive potentials determines the regularity of local minimizers of the interaction energy. In this paper, we show that if this repulsion is like Newtonian or more singular than Newtonian (but still locally integrable), then the local minimizers must be locally bounded densities (and even continuous for more singular than Newtonian repulsion). We prove this (and some other regularity results) by first showing that the potential function associated to a local minimizer solves an obstacle problem and then by using classical regularity results for such problems. |
| first_indexed | 2024-03-07T05:12:42Z |
| format | Journal article |
| id | oxford-uuid:dc1b5699-e67d-40da-ae34-f8e1937f64ea |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T05:12:42Z |
| publishDate | 2016 |
| publisher | Springer Science and Business Media LLC |
| record_format | dspace |
| spelling | oxford-uuid:dc1b5699-e67d-40da-ae34-f8e1937f64ea2022-03-27T09:15:27ZRegularity of local minimizers of the interaction energy via obstacle problemsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:dc1b5699-e67d-40da-ae34-f8e1937f64eaEnglishSymplectic ElementsSpringer Science and Business Media LLC2016Carrillo de la Plata, JADelgadino, MGMellet, AThe repulsion strength at the origin for repulsive/attractive potentials determines the regularity of local minimizers of the interaction energy. In this paper, we show that if this repulsion is like Newtonian or more singular than Newtonian (but still locally integrable), then the local minimizers must be locally bounded densities (and even continuous for more singular than Newtonian repulsion). We prove this (and some other regularity results) by first showing that the potential function associated to a local minimizer solves an obstacle problem and then by using classical regularity results for such problems. |
| spellingShingle | Carrillo de la Plata, JA Delgadino, MG Mellet, A Regularity of local minimizers of the interaction energy via obstacle problems |
| title | Regularity of local minimizers of the interaction energy via obstacle problems |
| title_full | Regularity of local minimizers of the interaction energy via obstacle problems |
| title_fullStr | Regularity of local minimizers of the interaction energy via obstacle problems |
| title_full_unstemmed | Regularity of local minimizers of the interaction energy via obstacle problems |
| title_short | Regularity of local minimizers of the interaction energy via obstacle problems |
| title_sort | regularity of local minimizers of the interaction energy via obstacle problems |
| work_keys_str_mv | AT carrillodelaplataja regularityoflocalminimizersoftheinteractionenergyviaobstacleproblems AT delgadinomg regularityoflocalminimizersoftheinteractionenergyviaobstacleproblems AT melleta regularityoflocalminimizersoftheinteractionenergyviaobstacleproblems |