We consider non-linear elliptic systems of the type div a(x,u,Du)=0 with Holder continuous dependence on x and 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.
The existence of regular boundary points for non-linear elliptic systems / Duzaar, F; Kristensen, J; Mingione, Giuseppe. - In: JOURNAL FÜR DIE REINE UND ANGEWANDTE MATHEMATIK. - ISSN 0075-4102. - 602:(2007), pp. 17-58. [10.1515/CRELLE.2007.002]
The existence of regular boundary points for non-linear elliptic systems
MINGIONE, Giuseppe
2007-01-01
Abstract
We consider non-linear elliptic systems of the type div a(x,u,Du)=0 with Holder continuous dependence on x and 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.File in questo prodotto:
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