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Sfb 288 Differential Geometry and Quantum Physics |
Abstract for Sfb Preprint No. 389
Partial regularity for nonlinear elliptic systems Frank Duzaar and Joseph F. Grotowski
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 in two situations: that of quasilinear elliptic systems with inhomogeneity obeying the natural growth condition, and that of fully nonlinear homogeneous systems. In the latter case our methods extend previous partial regularity results, directly establishing the optimal Hölder exponent for the derivative of a weak solution on its regular set
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