A curl-free improvement of the Rellich-Hardy inequality with weight
| Autor: | Hamamoto, Naoki, Takahashi, Futoshi |
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| Rok vydání: | 2021 |
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| Druh dokumentu: | Working Paper |
| Popis: | We consider the best constant in the Rellich-Hardy inequality (with a radial power weight) for curl-free vector fields on $\mathbb{R}^N$, originally found by Tertikas-Zographopoulos \cite{Tertikas-Z} for unconstrained fields. This inequality is considered as an intermediate between Hardy-Leray and Rellich-Leray inequalities. Under the curl-free condition, we compute the new explicit best constant in the inequality and prove the non-attainability of the constant. This paper is a sequel to \cite{CF_MAAN,CF_Re}. Comment: 30 pages |
| Databáze: | arXiv |
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