  We study the Dirichlet problem in Lipschitz domains and with boundary data in
Besov spaces, for divergence form strongly elliptic systems of arbitrary order,
with bounded, complex-valued coefficients. Our main result gives a sharp
condition on the local mean oscillations of the coefficients of the
differential operator and the unit normal to the boundary (which is
automatically satisfied if these functions belong to space VMO) guaranteeing
that the solution operator associated with this problem is an isomorphism.
