2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74190We prove two improved versions of the Hardy-Rellich inequality for the polyharmonic operator $(-Δ)^m$ involving the distance to the boundary. The first involves an infinite series improvement using logarithmic functions, while the second contains $L^2$ norms and involves as a coefficient the volume of the domain. We find explicit constants for these inequalities, and we prove their optimality in the first case.17 pagesAnalysis of PDEsSpectral Theory35J20; 26D10text