Boundary partial Holder regularity for elliptic systems with non-standard growth

Abstract

We investigate regular points on the boundaries of elliptic systems with non-standard growth, in particular, so-called Orlicz growth. A regular point on the boundary in this paper is a point for which a weak solution to a system is Holder continuous in a neighborhood. Here, we assume that the boundary of a domain and the boundary data are C1, and that a system has VMO (vanishing mean oscillation) type coefficients.

Keywords

• Partial regularity
• boundary regularity
• elliptic system
• non-standard growth