Boundary regularity for elliptic systems under a natural growth condition

Lisa Beck

paper

Boundary regularity for elliptic systems under a natural growth condition

arXiv:1002.1935

Abstract

We consider weak solutions $u \in u_{0} + W_{0}^{1, 2} (Ω, R^{N}) \cap L^{\infty} (Ω, R^{N})$ of second order nonlinear elliptic systems of the type $- d i v a (\cdot, u, D u) = b (\cdot, u, D u)$ in $Ω$ with an inhomogeneity satisfying a natural growth condition. In dimensions $n \in {2, 3, 4}$ we show that $H^{n - 1}$ -almost every boundary point is a regular point for $D u$ , provided that the boundary data and the coefficients are sufficiently smooth.

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