2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/126826We show that the sharp constant in the classical $n$-dimensional Hardy-Leray inequality can be improved for axisymmetric divergence-free fields, and find its optimal value. The same result is obtained for $n=2$ without the axisymmetry assumption.Classical Analysis and ODEsAnalysis of PDEs35R45,76D99, 26D15, 35R45,52A40, 47J20Sharp Hardy-Leray inequality for axisymmetric divergence-free fieldstext