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Discrete and Continuous Dynamical Systems - Series A (DCDS-A)
 

Lp regularity theory for linear elliptic systems

Pages: 121 - 134, Volume 18, Issue 1, May 2007

doi:10.3934/dcds.2007.18.121       Abstract        Full Text (206.1K)       Related Articles

Sun-Sig Byun - Department of Mathematical Sciences, Seoul National University, Seoul 151-747, South Korea (email)
Hongbin Chen - College of Sciences, Xian Jiaotong University, Xian 710049, China (email)
Mijoung Kim - Department of Mathematical Sciences, Seoul National University, Seoul 151-747, South Korea (email)
Lihe Wang - Department of Mathematics, University of Iowa, Iowa City, IA 52242, United States (email)

Abstract: 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, 35J25.

Received: April 2006;      Revised: November 2006;      Published: February 2007.