Acta mathematica scientia,Series B ›› 2010, Vol. 30 ›› Issue (5): 1541-1554.doi: 10.1016/S0252-9602(10)60147-6

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OPTIMAL INTERIOR PARTIAL REGULARITY FOR NONLINEAR ELLIPTIC SYSTEMS WITH DINI CONTINUOUS COEFFICIENTS

 QIU Ya-Lin1, 2, TAN Zhong1   

  1. 1.School of Mathematical Sciences, Xiamen University, Xiamen 361005, China
    2.School of Mathematics and Computing Science, Longyan University, Longyan 364000, China
  • Received:2008-06-27 Online:2010-09-20 Published:2010-09-20
  • Supported by:

    Supported by NSF of China (10531020) and the Education Department of Fujian Province (JK2009045) and the Program of 985 Innovation Engieering on Information in Xiamen University (2004-2007).

Abstract:

In this article, we consider nonlinear elliptic systems of divergence type with Dini continuous coefficients. The authors use a new method introduced by Duzaar and Grotowski, to prove partial regularity for weak solutions, based on a generalization of the technique of harmonic
approximation and directly establish the optimal H\"{o}lder exponent for the derivative of a weak solution on its regular set.

Key words: nonlinear elliptic systems, the natural growth condition, optimal partial regularity, A-harmonic approximation technique

CLC Number: 

  • 35J45
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