Optimal interior partial regularity for nonlinear elliptic systems: The method of $A$-harmonic approximation
Duzaar F, Grotowski JF (2000)
Publication Type: Journal article
Publication year: 2000
Journal
Publisher: Springer Verlag (Germany)
Book Volume: 103
Pages Range: 267-298
Journal Issue: 3
URI: http://www.springerlink.com/content/jvxdcub8hywkpyd5/fulltext.pdf
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.
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APA:
Duzaar, F., & Grotowski, J.F. (2000). Optimal interior partial regularity for nonlinear elliptic systems: The method of $A$-harmonic approximation. Manuscripta Mathematica, 103(3), 267-298. https://doi.org/10.1007/s002290070007
MLA:
Duzaar, Frank, and Joseph F. Grotowski. "Optimal interior partial regularity for nonlinear elliptic systems: The method of $A$-harmonic approximation." Manuscripta Mathematica 103.3 (2000): 267-298.
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