Lp regularity theory for linear elliptic systems

Sun-Sig Byun; Hongbin Chen; Mijoung Kim; Lihe Wang

doi:10.3934/dcds.2007.18.121

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2007, Volume 18, Issue 1: 121-134. Doi: 10.3934/dcds.2007.18.121

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L^p regularity theory for linear elliptic systems

1.
Department of Mathematical Sciences, Seoul National University, Seoul 151-747
2.
College of Sciences, Xian Jiaotong University, Xian 710049
3.
Department of Mathematics, University of Iowa, Iowa City, IA 52242

Received: March 31, 2006

Revised: October 31, 2006

Published: December 2006

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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.

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Mathematics Subject Classification: Primary: 35R05, 35R35; Secondary: 35J15, 35J25.

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L^p regularity theory for linear elliptic systems