Partial regularity for elliptic systems with critical growth
Summary: We prove a partial Hölder regularity result for weak solutions \(u : \Omega\to\mathbb{R}^N, N \geq 2\), to non-autonomous elliptic systems with general growth of the type \[ - \operatorname{div} a (x,u,Du) = b (x,u,Du)\quad \text{in } \Omega. \] The crucial point is that the operator \(a\) satisfies very weak regularity properties and general growth, while for the inhomogeneity \(b\) we allow a critical growth condition.
scientific article; zbMATH DE number 7602449
scientific article