The \(L^p\) Dirichlet problem for second order elliptic operators and a \(p\)-adapted square function (Q996251)

The authors consider operator \(L= \text{div\,}A\nabla+ b\nabla\), where \(b= (b_1,\dots, b_n)\) and \(A(X)= (a_{ij}(x))\) is strongly elliptic. They obtain solvability of the Dirichlet boundary value problem for a class of operators (in both divergence and non-divergence form) mentioned above, when data is in \(L^p\), for a full range of \(1< p<\infty\).