A remark on differentiability properties of solutions of some elliptic equations

A class of nondivergence unifrmly elliptic equations with measurable coefficients is studied. The oscillation of the coefficients near a Lebesgue point is assumed to be controlled by increasing functions satisfying Dini's condition. Under this assumption, slightly weaker than that of L. A. Caffarelli [2], a pointwise estimate for "good solutions" is established and related second order differentiability properties are pointed out.