The optimal weighted $W^{2, p}$ estimates of elliptic equation with non-compatible conditions

Yi Cao; Dong Li; Lihe Wang

doi:10.3934/cpaa.2011.10.561

Article Contents

2011, Volume 10, Issue 2: 561-570. Doi: 10.3934/cpaa.2011.10.561

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The optimal weighted $W^{2, p}$ estimates of elliptic equation with non-compatible conditions

1.
College of Science, Xi'an Jiaotong University, Xi'an, 710049
2.
Department of Mathematics, University of Iowa, 14 MacLean Hall, Iowa City, IA 52242
3.
Department of Mathematics, Shanghai Jiaotong University, Shang hai 200240

Received: March 31, 2010

Revised: July 31, 2010

Published: February 2011

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Abstract

In this paper we study uniformly elliptic equations with non-compatible conditions, where $\Omega$ is a bounded Lipchitz domain, and the right-hand side term and the boundary value of the elliptic equations belong to $L^p (p \geq 2)$ space. Then the optimal weighted $W^{2, p}$ estimates will be given by Whitney decomposition and $L^p$ estimates of non-tangential maximal function associated to solutions of the elliptic equations.

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Mathematics Subject Classification: Primary: 35J17, 35J60; Secondary: 47B25.

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References

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