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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Nonsymmetric systems
and area integral estimates


Authors: G. C. Verchota and A. L. Vogel
Journal: Proc. Amer. Math. Soc. 128 (2000), 453-462
MSC (1991): Primary 35J55, 31A25
Published electronically: September 27, 1999
MathSciNet review: 1616585
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Abstract: Even though the $L^2$ Dirichlet problem on Lipschitz domains is not always solvable for nonsymmetric strongly elliptic systems, so that many results and techniques from the symmetric systems are unavailable, there are some similarities with the symmetric systems. We show that the nontangential maximal function and the square function of a solution are equivalent and that there is a Fatou theorem for these solutions.


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Additional Information

G. C. Verchota
Affiliation: Department of Mathematics, Syracuse University, Syracuse, New York 13244

A. L. Vogel
Affiliation: Department of Mathematics, Syracuse University, Syracuse, New York 13244
Email: alvogel@syr.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04987-4
PII: S 0002-9939(99)04987-4
Keywords: Elliptic, bianalytic, area integral
Received by editor(s): September 16, 1997
Received by editor(s) in revised form: March 16, 1998
Published electronically: September 27, 1999
Additional Notes: The first author was partially supported by NSF Grant DMS-9706648.
Communicated by: Christopher D. Sogge
Article copyright: © Copyright 1999 American Mathematical Society