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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The regularity and Neumann problem for non-symmetric elliptic operators


Authors: Carlos E. Kenig and David J. Rule
Journal: Trans. Amer. Math. Soc. 361 (2009), 125-160
MSC (2000): Primary 35J25; Secondary 31A25
Published electronically: August 13, 2008
MathSciNet review: 2439401
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Abstract: We establish optimal $ L^p$ bounds for the non-tangential maximal function of the gradient of the solution to a second-order elliptic operator in divergence form, possibly non-symmetric, with bounded measurable coefficients independent of the vertical variable, on the domain above a Lipschitz graph in the plane, in terms of the $ L^p$-norm at the boundary of the tangential derivative of the Dirichlet data, or of the Neumann data.


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Additional Information

Carlos E. Kenig
Affiliation: Department of Mathematics, University of Chicago, 5734 S. University Avenue, Chicago, Illinois 60637
Email: cek@math.uchicago.edu

David J. Rule
Affiliation: Department of Mathematics, University of Chicago, 5734 S. University Avenue, Chicago, Illinois 60637
Address at time of publication: School of Mathematics, The University of Edinburgh, James Clerk Maxwell Building, The King’s Buildings, Mayfield Road, Edinburgh, EH9 3JZ, United Kingdom
Email: rule@uchicago.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04610-2
PII: S 0002-9947(08)04610-2
Received by editor(s): October 24, 2006
Published electronically: August 13, 2008
Additional Notes: The first author was supported in part by NSF grant number DMS-0456583
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.