# Boundary regularity for elliptic systems under a natural growth condition

created by beck on 09 Feb 2010
modified on 27 May 2013

[BibTeX]

Published Paper

Inserted: 9 feb 2010
Last Updated: 27 may 2013

Journal: Ann. Mat. Pura Appl.
Volume: 190
Number: 4
Pages: 553-588
Year: 2011
Doi: 10.1007/s10231-010-0163-0

Abstract:

We consider vector-valued weak solutions $u \in u_0 + W^{1,2}_0(\Omega,R^N) \cap L^{\infty}(\Omega,R^N)$ of second order nonlinear elliptic systems of the type $- div a (\cdot,u,Du) = b(\cdot,u,Du) \qquad in \Omega$ with an inhomogeneity satisfying a natural growth condition. In dimensions $n \in \{2,3,4\}$ we show that $\mathcal{H}^{n-1}$-almost every boundary point is a regular point for $Du$, provided that the boundary data and the coefficients are sufficiently smooth.