The $L^p$ regularity problem on Lipschitz domains
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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 $p$.References
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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
- MR Author ID: 227185
- Email: zshen2@email.uky.edu
- Received by editor(s): September 10, 2008
- Published electronically: October 6, 2010
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2737264