2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66637For a bounded convex domain Ωin R^N we prove refined Hardy inequalities that involve the Hardy potential corresponding to the distance to the boundary of Ω, the volume of $Ω$, as well as a finite number of sharp logarithmic corrections. We also discuss the best constant of these inequalities.11 pages, to appear in Commun. Contemp. MathAnalysis of PDEsSpectral Theory35J20 (Primary) 35P20, 35P99, 26D10 (Secondary)text