On the stability constant of Caffarelli-Kohn-Nirenberg inequality
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866929649771085824 |
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| author | Deng, Shengbing Tian, Xingliang |
| author_facet | Deng, Shengbing Tian, Xingliang |
| contents | By using a spectral analysis, we first show that the Caffarelli--Kohn--Nirenberg inequality with gradient remainder term of any order less than $4$ does not hold on the {\em Felli-Schneider} curve $b_{\mathrm{FS}}(a)$. Furthermore, we prove the existence of minimizers of sharp stability constant of Caffarelli--Kohn--Nirenberg inequality near the new curve $b^*_{\mathrm{FS}}(a)(>b_{\mathrm{FS}}(a))$, which extends the work of Wei and Wu [Math. Z., 2024] to a sightly larger region. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_04111 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the stability constant of Caffarelli-Kohn-Nirenberg inequality Deng, Shengbing Tian, Xingliang Analysis of PDEs 35P30, 26D10, 49J40 By using a spectral analysis, we first show that the Caffarelli--Kohn--Nirenberg inequality with gradient remainder term of any order less than $4$ does not hold on the {\em Felli-Schneider} curve $b_{\mathrm{FS}}(a)$. Furthermore, we prove the existence of minimizers of sharp stability constant of Caffarelli--Kohn--Nirenberg inequality near the new curve $b^*_{\mathrm{FS}}(a)(>b_{\mathrm{FS}}(a))$, which extends the work of Wei and Wu [Math. Z., 2024] to a sightly larger region. |
| title | On the stability constant of Caffarelli-Kohn-Nirenberg inequality |
| topic | Analysis of PDEs 35P30, 26D10, 49J40 |
| url | https://arxiv.org/abs/2308.04111 |