Boundary regularity for elliptic systems under a natural growth condition

Details Boundary regularity for elliptic systems under a natural growth condition Boundary regularity for elliptic systems under a natural growth condition

2010-02-09

arxiv.org/abs/1002.1935v3

Mathematics

Analysis of PDEs

revised version, accepted for publication in Ann. Mat. Pura Appl

Scientific paper

We consider 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 $- div a (\cdot, u, Du) = b(\cdot,u,Du)$ 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.

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