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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.28982 |
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| _version_ | 1866910267374305280 |
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| author | Neumayer, Robin |
| author_facet | Neumayer, Robin |
| contents | The goal of this short note is to prove qualitative stability for a family of trace Sobolev inequalities first proven by Carlen \& Loss for $p=2$ and by Maggi and the author for $p\in (1,n)$. This answers an open problem raised in a recent paper of Fan, Li \& Zhang, and in conjunction with their local analysis, yields sharp quantitative stability for this family of inequalities when $p=2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_28982 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Qualitative stability for a family of trace Sobolev inequalities Neumayer, Robin Analysis of PDEs The goal of this short note is to prove qualitative stability for a family of trace Sobolev inequalities first proven by Carlen \& Loss for $p=2$ and by Maggi and the author for $p\in (1,n)$. This answers an open problem raised in a recent paper of Fan, Li \& Zhang, and in conjunction with their local analysis, yields sharp quantitative stability for this family of inequalities when $p=2$. |
| title | Qualitative stability for a family of trace Sobolev inequalities |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2605.28982 |