A regularity result for stationary electrorheological fluids in two dimensions

Abstract

Abstract We prove C 1, α ‐regularity for the strong solution to a non‐linear system of partial differential equations modeling electrorheological fluids in the stationary case which has been constructed by Ettwein and Ettwein‐Růžička [Elektrorheologische Flüssigkeiten: Existenz starker Lösungen in zweidimensionalen Gebieten. Diplomarbeit, Universität Freiburg, 2002; Geometric Analysis and Nonlinear Partial Differential Equations , Hildebrandt S, Karcher H (eds). Springer: Berlin–Heidelberg–New York, 2003; 591–602]. Copyright © 2004 John Wiley & Sons, Ltd.