We obtain regularity results for solutions to Pu = f when P is a kth order elliptic differential operator with the property that both P and Pt have coefficients that are continuous, with a modulus of continuity satisfying a Dini-type condition. Operators of this form arise in the study of regularity of functions that are known to be regular along the leaves of several foliations, such as arise in Anosov systems. The results here complement some previous results of the author and J. Rauch.