On the range of elliptic, second order, nonvariational operators in Sobolev spaces

The subfamilyR(p, Ω) of the class of second order, uniformly elliptic, non variational operators L with bounded measurable coefficients, such that L(W^{2, p} (Ω)) is dense in L^p (Ω), is studied. Sufficient and necessary and sufficient conditions are given, for L to belong toR(p, Ω). An operator L of the class above and not inR(p, Ω) is constructed. Entrata in Redazione il 5 ottobre 1998.