Let us consider some regularity properties for solutions of some elliptic systems. The coefficients of the higher order derivatives could be discontinuous, in particular we study the vanishing mean oscillation class, considered at first by D. Sarason in the note “ On functions of vanishing mean oscillation” T.A.M.S. 207 (1975).

This class of functions has been very useful for many authors to obtain regularity results for istance for linear elliptic equations in nondivergence form, in divergence form, for parabolic equations and for ultraparabolic equations.