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

Pages: 561 - 570, Volume 10, Issue 2, March 2011

doi:10.3934/cpaa.2011.10.561       Abstract        References        Full Text (382.1K)       Related Articles

Yi Cao - College of Science, Xi'an Jiaotong University, Xi'an, 710049, China (email)
Dong Li - Department of Mathematics, University of Iowa, 14 MacLean Hall, Iowa City, IA 52242, China (email)
Lihe Wang - Department of Mathematics, Shanghai Jiaotong University, Shang hai 200240, China (email)

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.

Keywords:  Elliptic equations, bounded Lipchitz domain, non-compatible conditions.
Mathematics Subject Classification:  Primary: 35J17, 35J60; Secondary: 47B25.

Received: April 2010;      Revised: August 2010;      Published: December 2010.

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