manuscripta mathematica

, Volume 103, Issue 3, pp 267–298 | Cite as

Optimal interior partial regularity¶for nonlinear elliptic systems: the method of A-harmonic approximation

  • Frank Duzaar
  • Joseph F. Grotowski

Abstract:

We consider nonlinear elliptic systems of divergence type. We provide a new method for proving partial regularity for weak solutions, based on a generalization of the technique of harmonic approximation. This method is applied to both homogeneous and inhomogeneous systems, in the latter case with inhomogeneity obeying the natural growth condition. Our methods extend previous partial regularity results, directly establishing the optimal Hölder exponent for the derivative of a weak solution on its regular set. We also indicate how the technique can be applied to further simplify the proof of partial regularity for quasilinear elliptic systems.

Mathematics Subject Classification (2000): 35J45 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Frank Duzaar
    • 1
  • Joseph F. Grotowski
    • 1
  1. 1.Mathematisches Institut der Friedrich-Alexander-Universität Erlangen–Nürnberg, Bismarckstr. 1 1/2, 91054 Erlangen, Germany.¶E-mail: duzaar@mi.uni-erlangen.de; grotow@mi.uni-erlangen.deDE

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