2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63158We study an elliptic differential operator A on a manifold with conic points. Assuming A to be defined on the smooth functions supported away from the singularities, we first address the question of possible closed extensions of A to L^p Sobolev spaces and then explain how additional ellipticity conditions ensure maximal regularity for the operator A. Investigating the Lipschitz continuity of the maps f(u)=|u|^α, with real α\ge 1, and f(u)=u^α, with αa natural number, and using a result of Clément and Li, we finally show unique solvability of a quasilinear equation of the form \dot{u} - a(u) Δu = f(u) in suitable spaces.18 pages (revised version, 23/04/'02)Analysis of PDEsFunctional Analysis58J40 (Primary) 35K65, 47A10 (Secondary)text