Gilbarg-Serrin equation and Lipschitz regularity

We discuss conditions for Lipschitz and C1 regularity of solutions for a uniformly elliptic equation in divergence form. We focus on coefficients having the form that was introduced by Gilbarg & Serrin. In particular, we find cases where Lipschitz or C1 regularity holds but the coefficients are not Dini continuous, or do not even have Dini mean oscillation. The form of the coefficients also enables us to obtain specific conditions and examples for which there exists a weak solution that is not Lipschitz continuous.