Mathematical Research Letters

Volume 16 (2009)

Number 5

On Hofmann’s bilinear estimate

Pages: 753 – 760

DOI: http://dx.doi.org/10.4310/MRL.2009.v16.n5.a1

Author

Pascal Auscher (Université de Paris-Sud)

Abstract

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.

Keywords

elliptic systems, Dirichlet problem, quadratic estimates, Carleson measures

2010 Mathematics Subject Classification

35J25, 35J56, 42B25, 47N20

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