Regularity results for differential forms solving degenerate elliptic systems
This paper deals with the regularity of weak solutions for some classes of degenerate elliptic problems on bounded domains. In the first part, the authors are concerned with a possible degeneracy at the origin like the \(p\)-Laplace or even systems of Uhlenbeck structure. The main tools in the proofs are the \(p\)-harmonic approximation lemma and the \(a\)-approximation method. Next, the authors present a unified and simplified proof of the partial regularity result for the sub- and the superquadratic case. The theoretical arguments developed in this paper could also serve to deal with other regularity issues for differential forms, such as partial regularity (and dimension reduction for the singular set) in the context of parabolic systems or Calderon-Zygmund-type estimates with nonstandard growth.
scientific article; zbMATH DE number 6145938
scientific article