## The regularity and Neumann problem for non-symmetric elliptic operators

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- by Carlos E. Kenig and David J. Rule PDF
- Trans. Amer. Math. Soc.
**361**(2009), 125-160 Request permission

## 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.## References

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## Additional Information

**Carlos E. Kenig**- Affiliation: Department of Mathematics, University of Chicago, 5734 S. University Avenue, Chicago, Illinois 60637
- MR Author ID: 100230
- 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
- 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
- © Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc.
**361**(2009), 125-160 - MSC (2000): Primary 35J25; Secondary 31A25
- DOI: https://doi.org/10.1090/S0002-9947-08-04610-2
- MathSciNet review: 2439401