2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/230467Using the framework of a previous article joint with Axelsson and McIntosh, we extend to systems two results of S. Hofmann for real symmetric equations and their perturbations going back to a work of B. Dahlberg for Laplace's equation on Lipschitz domains, The first one is a certain bilinear estimate for a class of weak solutions and the second is a criterion which allows to identify the domain of the generator of the semi-group yielding such solutions.updated incorporating suggestions of the referee. some refercences added. to appear in Math. Research LettersAnalysis of PDEsClassical Analysis and ODEsFunctional Analysis35J25, 35J55, 47N20, 42B25text