Calculus of Variations and Geometric Measure Theory
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F. Duzaar - J. Kristensen - G. Mingione

The existence of regular boundary points for non-linear elliptic systems

created by mingione on 29 Sep 2012

[BibTeX]

Published Paper

Inserted: 29 sep 2012
Last Updated: 29 sep 2012

Journal: J. Rein. Ang. Math. (Crelles J.)
Volume: 602
Pages: 17-58
Year: 2007

Abstract:

We consider non-linear elliptic systems of the type \[ -\mbox{div}\, \ a(x,u,Du)=0 \] with H\"older continuous dependence on $(x,u)$, and give conditions guaranteeing that $H^{n-1}$-almost every boundary point is a regular point for the gradient of solutions to related Dirichlet problems. We also introduce a new comparison technique, in order to deal with difference quotients.

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