A short review on Improvements and stability for some interpolation inequalities
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913322921623552 |
|---|---|
| author | Dolbeault, Jean Esteban, Maria J. Figalli, Alessio Frank, Rupert Loss, Michael |
| author_facet | Dolbeault, Jean Esteban, Maria J. Figalli, Alessio Frank, Rupert Loss, Michael |
| contents | In this paper, we present recent stability results with explicit and dimensionally sharp constants and optimal norms for the Sobolev inequality and for the Gaussian logarithmic Sobolev inequality obtained by the authors in [24]. The stability for the Gaussian logarithmic Sobolev inequality was obtained as a byproduct of the stability for the Sobolev inequality. Here we give a new, direct, alternative proof. We also discuss improved versions of interpolation inequalities based on the carré du champ method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_08527 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A short review on Improvements and stability for some interpolation inequalities Dolbeault, Jean Esteban, Maria J. Figalli, Alessio Frank, Rupert Loss, Michael Analysis of PDEs 49J40 (Primary) 26D10, 35A23, 58E35 (Secondary) In this paper, we present recent stability results with explicit and dimensionally sharp constants and optimal norms for the Sobolev inequality and for the Gaussian logarithmic Sobolev inequality obtained by the authors in [24]. The stability for the Gaussian logarithmic Sobolev inequality was obtained as a byproduct of the stability for the Sobolev inequality. Here we give a new, direct, alternative proof. We also discuss improved versions of interpolation inequalities based on the carré du champ method. |
| title | A short review on Improvements and stability for some interpolation inequalities |
| topic | Analysis of PDEs 49J40 (Primary) 26D10, 35A23, 58E35 (Secondary) |
| url | https://arxiv.org/abs/2402.08527 |