In this note we prove local Lp-regularity for the highest-order derivatives of an elliptic system of arbitrary order in nondivergence form where the coefficients of the principal part are taken in the space of Sarason vanishing mean oscillation (VMO). Lower-order coefficients and the known term belong to suitable Lebesgue spaces. As a consequence, we obtain Hölder regularity results.
"Local Hölder regularity for solutions of elliptic systems." Duke Math. J. 113 (2) 385 - 397, 1 June 2002. https://doi.org/10.1215/S0012-7094-02-11327-1