W^{2,p}-regularity for a class of elliptic second order equations with discontinuous coefficients

Abstract

We prove a well-posedness result in the intersection class of W2,p with W01,p for the Dirichlet problem (*) below. We assume L to be an elliptic second order operator with discontinuous coefficients and lower order terms. The paper extends a recent result (see [1], [2]) for operators restricted to leading terms.