Improved Interpolation Inequalities and Stability
For exponents in the subcritical range, we revisit some optimal interpolation inequalities on the sphere with carré du champ methods and use the remainder terms to produce improved inequalities. The method provides us with lower estimates of the optimal constants in the symmetry breaking range and s...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2020-05-01
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| Series: | Advanced Nonlinear Studies |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/ans-2020-2080 |
| _version_ | 1817997008033546240 |
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| author | Dolbeault Jean Esteban Maria J. |
| author_facet | Dolbeault Jean Esteban Maria J. |
| author_sort | Dolbeault Jean |
| collection | DOAJ |
| description | For exponents in the subcritical range, we revisit some optimal interpolation inequalities on the sphere with carré du champ methods and use the remainder terms to produce improved inequalities. The method provides us with lower estimates of the optimal constants in the symmetry breaking range and stability estimates for the optimal functions. Some of these results can be reformulated in the Euclidean space using the stereographic projection. |
| first_indexed | 2024-04-14T02:31:52Z |
| format | Article |
| id | doaj.art-2b90235999ca48a3aa9e3e579e630bfa |
| institution | Directory Open Access Journal |
| issn | 1536-1365 2169-0375 |
| language | English |
| last_indexed | 2024-04-14T02:31:52Z |
| publishDate | 2020-05-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advanced Nonlinear Studies |
| spelling | doaj.art-2b90235999ca48a3aa9e3e579e630bfa2022-12-22T02:17:39ZengDe GruyterAdvanced Nonlinear Studies1536-13652169-03752020-05-0120227729110.1515/ans-2020-2080Improved Interpolation Inequalities and StabilityDolbeault Jean0Esteban Maria J.1CEREMADE (CNRS UMR no 7534), PSL University, Université Paris-Dauphine, Place de Lattre de Tassigny, 75775Paris16, FranceCEREMADE (CNRS UMR no 7534), PSL University, Université Paris-Dauphine, Place de Lattre de Tassigny, 75775Paris16, FranceFor exponents in the subcritical range, we revisit some optimal interpolation inequalities on the sphere with carré du champ methods and use the remainder terms to produce improved inequalities. The method provides us with lower estimates of the optimal constants in the symmetry breaking range and stability estimates for the optimal functions. Some of these results can be reformulated in the Euclidean space using the stereographic projection.https://doi.org/10.1515/ans-2020-2080interpolationgagliardo–nirenberg inequalitiessobolev inequalitylogarithmic sobolev inequalitypoincaré inequalityheat equationnonlinear diffusion26d10 46e35 58e35 |
| spellingShingle | Dolbeault Jean Esteban Maria J. Improved Interpolation Inequalities and Stability Advanced Nonlinear Studies interpolation gagliardo–nirenberg inequalities sobolev inequality logarithmic sobolev inequality poincaré inequality heat equation nonlinear diffusion 26d10 46e35 58e35 |
| title | Improved Interpolation Inequalities and Stability |
| title_full | Improved Interpolation Inequalities and Stability |
| title_fullStr | Improved Interpolation Inequalities and Stability |
| title_full_unstemmed | Improved Interpolation Inequalities and Stability |
| title_short | Improved Interpolation Inequalities and Stability |
| title_sort | improved interpolation inequalities and stability |
| topic | interpolation gagliardo–nirenberg inequalities sobolev inequality logarithmic sobolev inequality poincaré inequality heat equation nonlinear diffusion 26d10 46e35 58e35 |
| url | https://doi.org/10.1515/ans-2020-2080 |
| work_keys_str_mv | AT dolbeaultjean improvedinterpolationinequalitiesandstability AT estebanmariaj improvedinterpolationinequalitiesandstability |