Characterization of fractional Sobolev--Poincaré and (localized) Hardy inequalities
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866913467528642560 |
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| author | Sk, Firoj |
| author_facet | Sk, Firoj |
| contents | In this paper, we prove capacitary versions of the fractional Sobolev--Poincaré inequalities. We characterize localized variant of the boundary fractional Sobolev--Poincaré inequalities through uniform fatness condition of the domain in $\mathbb{R}^n$. Existence type results on the fractional Hardy inequality are established in the supercritical case $sp>n$ for $s\in(0,1)$, $p>1$. Characterization of the fractional Hardy inequality through weak supersolution of the associate problem is also addressed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_06636 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Characterization of fractional Sobolev--Poincaré and (localized) Hardy inequalities Sk, Firoj Analysis of PDEs Functional Analysis 46E35, 35A23, 42B25, 31B15 In this paper, we prove capacitary versions of the fractional Sobolev--Poincaré inequalities. We characterize localized variant of the boundary fractional Sobolev--Poincaré inequalities through uniform fatness condition of the domain in $\mathbb{R}^n$. Existence type results on the fractional Hardy inequality are established in the supercritical case $sp>n$ for $s\in(0,1)$, $p>1$. Characterization of the fractional Hardy inequality through weak supersolution of the associate problem is also addressed. |
| title | Characterization of fractional Sobolev--Poincaré and (localized) Hardy inequalities |
| topic | Analysis of PDEs Functional Analysis 46E35, 35A23, 42B25, 31B15 |
| url | https://arxiv.org/abs/2204.06636 |