On Hofmann's bilinear estimate

Pascal Auscher (1)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay

Using 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.

Mots clés: elliptic systems; Dirichlet problem; quadratic estimates; Carleson measures

Domaines: Equations aux dérivées partielles [math.AP]; Analyse fonctionnelle [math.FA]; Analyse classique [math.CA]

Pascal Auscher. On Hofmann's bilinear estimate. Mathematical Research Letters, 2009, 16 (5), pp.755--763. ⟨hal-00347845v3⟩