Regularity results for differential forms solving degenerate elliptic systems

We present a partial Hölder regularity result for differential forms solving degenerate systems on bounded domains in the weak sense. Here certain continuity, monotonicity, growth and structure condition are imposed on the coefficients, including an asymptotic Uhlenbeck behavior close to the origin. Pursuing an approach of Duzaar and Mingione (J Math Anal Appl 352(1):301–335, 2009), we combine non-degenerate and degenerate harmonic-type approximation lemmas for the proof of the partial regularity result, giving several extensions and simplifications. In particular, we benefit from a direct proof of the approximation lemma (Diening et al. 2010) that simplifies and unifies the proof in the power growth case. Moreover, we give the dimension reduction for the set of singular points.