Calculus of Variations and Geometric Measure Theory
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M. Foss - G. Mingione

Partial continuity for elliptic problems

created by mingione on 29 Sep 2012

[BibTeX]

Published Paper

Inserted: 29 sep 2012
Last Updated: 29 sep 2012

Journal: Ann. Inst. H. Poincaré Anal. Non Linéaire
Volume: 25
Pages: 471-503
Year: 2008

Abstract:

We prove the partial H\"older continuity for solutions to elliptic systems and for minimizers of quasi-convex integrals, under the assumption of continuous coefficients. The proof relies upon an iteration scheme of a decay estimate for a new type of excess functional measuring the oscillations in the solution and its gradient. To establish the decay estimate, we use the technique of A-harmonic approximation, based on Duzaar & Steffen's A-harmonic approximation lemma

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