Interpolation inequalities on the sphere and phase transition: rigidity, symmetry and symmetry breaking
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866912061142859776 |
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| author | Dagher, Esther Bou Dolbeault, Jean |
| author_facet | Dagher, Esther Bou Dolbeault, Jean |
| contents | This paper is devoted to the study of phase transitions associated to a large family of Gagliardo-Nirenberg-Sobolev interpolation inequalities on the sphere depending on one parameter. We characterize symmetry and symmetry breaking regimes, with a phase transition that can be of first or second order. We establish various new results and study the qualitative properties of the branches of solutions to the Euler-Lagrange equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_16878 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Interpolation inequalities on the sphere and phase transition: rigidity, symmetry and symmetry breaking Dagher, Esther Bou Dolbeault, Jean Analysis of PDEs 58J05, 35B06, 26D10 This paper is devoted to the study of phase transitions associated to a large family of Gagliardo-Nirenberg-Sobolev interpolation inequalities on the sphere depending on one parameter. We characterize symmetry and symmetry breaking regimes, with a phase transition that can be of first or second order. We establish various new results and study the qualitative properties of the branches of solutions to the Euler-Lagrange equations. |
| title | Interpolation inequalities on the sphere and phase transition: rigidity, symmetry and symmetry breaking |
| topic | Analysis of PDEs 58J05, 35B06, 26D10 |
| url | https://arxiv.org/abs/2210.16878 |