In this paper we prove a partial Hölder regularity result for weak solutions u : Ω → RN, N ≥ 2, to non-autonomous elliptic systems with general growth of the type: -div a(x, u,Du) = b(x, u,Du) in Ω. The crucial point is that the operator a satisfies very weak regularity properties and a general growth, while the inhomogeneity b has a controllable growth.
Partial regularity result for non-autonomous elliptic systems with general growth / Isernia, T.; Leone, C.; Verde, A.. - In: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS. - ISSN 1534-0392. - 20:12(2021), pp. 4271-4305. [10.3934/cpaa.2021160]