  We use the method of layer potentials to study the $R_2$ Regularity problem
and the $D_2$ Dirichlet problem for second order elliptic equations of the form
$\mathcal{L}u=0$, with lower order coefficients, in bounded Lipschitz domains.
For $R_2$ we establish existence and uniqueness assuming that $\mathcal{L}$ is
of the form $\mathcal{L}u=-\text{div}(A\nabla u+bu)+c\nabla u+du$, where the
matrix $A$ is uniformly elliptic and H\"older continuous, $b$ is H\"older
continuous, and $c,d$ belong to Lebesgue classes and they satisfy either the
condition $d\geq\text{div}b$, or $d\geq\text{div}c$ in the sense of
distributions. In particular, $A$ is not assumed to be symmetric, and there is
no smallness assumption on the norms of the lower order coefficients. We also
show existence and uniqueness for $D_2$ for the adjoint equations
$\mathcal{L}^tu=0$.
