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January  2007, 18(1): 121-134. doi: 10.3934/dcds.2007.18.121

Lp regularity theory for linear elliptic systems

Sun-Sig Byun 1, , Hongbin Chen 2, , Mijoung Kim 1, and  Lihe Wang 3,

1. 

Department of Mathematical Sciences, Seoul National University, Seoul 151-747, South Korea, South Korea
2. 

College of Sciences, Xian Jiaotong University, Xian 710049, China
3. 

Department of Mathematics, University of Iowa, Iowa City, IA 52242, United States

Received  April 2006 Revised  November 2006 Published  February 2007

We consider the conormal derivative problem for an elliptic system in divergence form with discontinuous coefficients in a more general geometric setting. We obtain the $L^{p}$, $1 < p <\infty$, regularity of the maximum order derivatives of the weak solutions for such a problem.
Keywords: $L^{p}$ estimates, elliptic system, BMO space, Reifenberg Domain..
Mathematics Subject Classification: Primary: 35R05, 35R35; Secondary: 35J15, 35J2.
Citation: Sun-Sig Byun, Hongbin Chen, Mijoung Kim, Lihe Wang. Lp regularity theory for linear elliptic systems. Discrete & Continuous Dynamical Systems, 2007, 18 (1) : 121-134. doi: 10.3934/dcds.2007.18.121
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