  In the present article, we purpose a method to deal with
Dahlberg-Kenig-Pipher (DPK) operators in boundary value problems on the upper
half plane.
  We give a nice subclass of the weak DKP operators that generates the full
class of weak DKP operators under bi-Lipschitz changes of variable on $\mathbb
R^n_+$ that fixe the boundary $\mathbb R^{n-1}$. Therefore, if one wants to
prove a property on DKP operators which is stable by bi-Lipschitz
transformations, one can directly assume that the operator belongs to the
subclass. Our method gives an alternative proof to some past results and
self-improves others beyond the existing literature.
