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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

Homogenization of elliptic systems with Neumann boundary conditions


Authors: Carlos E. Kenig, Fanghua Lin and Zhongwei Shen
Journal: J. Amer. Math. Soc. 26 (2013), 901-937
MSC (2010): Primary 35J57
Published electronically: March 27, 2013
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Abstract: For a family of second-order elliptic systems with rapidly oscillating periodic coefficients in a $ C^{1,\alpha }$ domain, we establish uniform $ W^{1,p}$ estimates, Lipschitz estimates, and nontangential maximal function estimates on solutions with Neumann boundary conditions.


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Additional Information

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

Fanghua Lin
Affiliation: Courant Institute of Mathematical Sciences, New York University, New York, New York 10012
Email: linf@cims.nyu.edu

Zhongwei Shen
Affiliation: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506
Email: zshen2@email.uky.edu

DOI: http://dx.doi.org/10.1090/S0894-0347-2013-00769-9
PII: S 0894-0347(2013)00769-9
Received by editor(s): October 28, 2010
Received by editor(s) in revised form: February 26, 2013
Published electronically: March 27, 2013
Additional Notes: The first author was supported in part by NSF grant DMS-0968472
The second author was supported in part by NSF grant DMS-0700517
The third author was supported in part by NSF grant DMS-0855294
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.