A curl-free improvement of the Rellich-Hardy inequality with weight

Naoki Hamamoto; Futoshi Takahashi

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arXiv · 2101.01878

A curl-free improvement of the Rellich-Hardy inequality with weight

Naoki Hamamoto·Futoshi Takahashi

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Abstract

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}.

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Naoki Hamamoto, Futoshi Takahashi. 2021-01-06. A curl-free improvement of the Rellich-Hardy inequality with weight. https://arxiv.org/abs/2101.01878

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