The Trudinger type inequality in fractional boundary Hardy inequality
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912898191720448 |
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| author | Adimurthi Roy, Prosenjit Sahu, Vivek |
| author_facet | Adimurthi Roy, Prosenjit Sahu, Vivek |
| contents | We establish Trudinger-type inequality in the context of fractional boundary Hardy-type inequality for the case $sp=d$, where $p>1, ~ s \in (0,1)$ on a bounded Lipschitz domain $Ω\subset \mathbb{R}^d$. In particular, we establish fractional version of Trudinger-type inequality with an extra singular function, namely $d$-th power of the distance function from $\partial Ω$ in the denominator of the integrand. The case $d=1$, as it falls in the category $sp=1$, becomes more delicate where an extra logarithmic correction is required together with subtraction of an average term. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_19362 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Trudinger type inequality in fractional boundary Hardy inequality Adimurthi Roy, Prosenjit Sahu, Vivek Analysis of PDEs 46E35 (Primary), 26D15 (Secondary) We establish Trudinger-type inequality in the context of fractional boundary Hardy-type inequality for the case $sp=d$, where $p>1, ~ s \in (0,1)$ on a bounded Lipschitz domain $Ω\subset \mathbb{R}^d$. In particular, we establish fractional version of Trudinger-type inequality with an extra singular function, namely $d$-th power of the distance function from $\partial Ω$ in the denominator of the integrand. The case $d=1$, as it falls in the category $sp=1$, becomes more delicate where an extra logarithmic correction is required together with subtraction of an average term. |
| title | The Trudinger type inequality in fractional boundary Hardy inequality |
| topic | Analysis of PDEs 46E35 (Primary), 26D15 (Secondary) |
| url | https://arxiv.org/abs/2410.19362 |