2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/221945We show that elliptic second order operators $A$ of divergence type fulfill maximal parabolic regularity on distribution spaces, even if the underlying domain is highly non-smooth, the coefficients of $A$ are discontinuous and $A$ is complemented with mixed boundary conditions. Applications to quasilinear parabolic equations with non-smooth data are presented.39 pages, 4 postscript figuresAnalysis of PDEs35A05, 35B65 (Primary), 35K15, 35K20 (Secondary)text