Logarithmic Sobolev inequalities: a review on stability and instability results; logarithmic uncertainty principle
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912705864007680 |
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| author | Brigati, Giovanni Dolbeault, Jean Simonov, Nikita |
| author_facet | Brigati, Giovanni Dolbeault, Jean Simonov, Nikita |
| contents | In this paper, we review recent results on stability and instability in logarithmic Sobolev inequalities, with a particular emphasis on strong norms. We consider several versions of these inequalities on the Euclidean space, for the Lebesgue and the Gaussian measures, and discuss their differences in terms of moments and stability. We give new and direct proofs, as well as examples and discuss the stability of a logarithmic uncertainty principle. Although we do not cover all aspects of the topic, we hope to contribute to establishing the state of the art. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_08658 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Logarithmic Sobolev inequalities: a review on stability and instability results; logarithmic uncertainty principle Brigati, Giovanni Dolbeault, Jean Simonov, Nikita Analysis of PDEs Functional Analysis 39B62, 47J20, 49J40, 35A23 In this paper, we review recent results on stability and instability in logarithmic Sobolev inequalities, with a particular emphasis on strong norms. We consider several versions of these inequalities on the Euclidean space, for the Lebesgue and the Gaussian measures, and discuss their differences in terms of moments and stability. We give new and direct proofs, as well as examples and discuss the stability of a logarithmic uncertainty principle. Although we do not cover all aspects of the topic, we hope to contribute to establishing the state of the art. |
| title | Logarithmic Sobolev inequalities: a review on stability and instability results; logarithmic uncertainty principle |
| topic | Analysis of PDEs Functional Analysis 39B62, 47J20, 49J40, 35A23 |
| url | https://arxiv.org/abs/2504.08658 |