Partial regularity up to the boundary for solutions of subquadratic elliptic systems

Abstract

In this paper, we are concerned with the nonlinear elliptic systems in divergence form under controllable growth condition. We prove that the weak solution u is locally Hölder continuous besides a singular set by using the direct method and classical Morrey-type estimates. Here the Hausdorff dimension of the singular set is less than n-p{n-p}. This result not only holds in the interior, but also holds up to the boundary.

Keywords

• subquadratic elliptic systems
• controllable growth condition
• higher integrability
• partial regularity
• 35j60