2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62410We prove that the index formula for $b$-elliptic cone differential operators given by M. Lesch holds verbatim for operators whose coefficients are not necessarily independent of the normal variable near the boundary. We also show that, for index purposes, the operators can always be considered on weighted Sobolev spaces.Analysis of PDEsFunctional Analysis58J20; 35J70; 58J35text