Fractional Hardy inequality with singularity on submanifold
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866918333099540480 |
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| author | Adimurthi Roy, Prosenjit Sahu, Vivek |
| author_facet | Adimurthi Roy, Prosenjit Sahu, Vivek |
| contents | We establish fractional Hardy inequality on bounded domains in $\mathbb{R}^{d}$ with inverse of distance function from smooth boundary of codimension $k$, where $k=2, \dots,d$, as weight function. The case $sp=k$ is the critical case, where optimal logarithmic corrections are required. All the other cases of $sp<k$ and $sp>k$ are also addressed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_10863 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fractional Hardy inequality with singularity on submanifold Adimurthi Roy, Prosenjit Sahu, Vivek Analysis of PDEs 46E35 (Primary), 26D15 (Secondary) We establish fractional Hardy inequality on bounded domains in $\mathbb{R}^{d}$ with inverse of distance function from smooth boundary of codimension $k$, where $k=2, \dots,d$, as weight function. The case $sp=k$ is the critical case, where optimal logarithmic corrections are required. All the other cases of $sp<k$ and $sp>k$ are also addressed. |
| title | Fractional Hardy inequality with singularity on submanifold |
| topic | Analysis of PDEs 46E35 (Primary), 26D15 (Secondary) |
| url | https://arxiv.org/abs/2407.10863 |