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

2021/01/06 by Hamamoto, Naoki, Takahashi, Futoshi · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2101.01878

Abstract

We consider the best constant in the Rellich-Hardy inequality (with a radial power weight) for curl-free vector fields on ℝ^N, originally found by Tertikas-Zographopoulos \citeTertikas-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 \citeCF_MAAN,CF_Re.

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