references for 2nd order elliptic boundary value problems

Question

Let $\Omega \subset \mathbf{R}^2$ open and bounded with smooth boundary $\partial \Omega$. Suppose that we have a second order differential operator $L$ on $\Omega$ with smooth coefficients. I'm interested in elliptic regularity theory for the equation $Lu=f$ in $\Omega$ with boundary conditions $Bu=g$ on $\partial \Omega$ where $Bu= b_0 u + b_1 \partial_x u + b_2 \partial_y u$ with $b_i$ smooth. All the problems I studied so far and that were taught in the lectures only concern operators $L$ in divergence form (without lower orders) and Dirichlet boundary conditions. Then, it was shown by the technique of difference quotients that one obtains higher interior regularity for weak solutions and how to extend this to the boundary using local charts and flat boundaries. I now wonder if there is a canonical way how to extend this strategy to operators $L$ with lower order terms and general boundary conditions $B$.