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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

The $ L^p$ regularity problem on Lipschitz domains


Authors: Joel Kilty and Zhongwei Shen
Journal: Trans. Amer. Math. Soc. 363 (2011), 1241-1264
MSC (2000): Primary 35J55, 35J40
DOI: https://doi.org/10.1090/S0002-9947-2010-05076-7
Published electronically: October 6, 2010
MathSciNet review: 2737264
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Abstract: This paper contains two results on the $ L^p$ regularity problem on Lipschitz domains. For second order elliptic systems and $ 1<p<\infty$, we prove that the solvability of the $ L^p$ regularity problem is equivalent to that of the $ L^{p^\prime}$ Dirichlet problem. For higher order elliptic equations and systems, we show that if $ p>2$, the solvability of the $ L^p$ regularity problem is equivalent to a weak reverse Hölder condition with exponent $ p$.


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Additional Information

Joel Kilty
Affiliation: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506
Address at time of publication: Department of Mathematics, Centre College, Danville, Kentucky 40422
Email: jkilty@ms.uky.edu, joel.kilty@centre.edu

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

DOI: https://doi.org/10.1090/S0002-9947-2010-05076-7
Keywords: Lipschitz domains, regularity problem, Dirichlet problem
Received by editor(s): September 10, 2008
Published electronically: October 6, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.