A priori estimate for degenerate elliptic equation.

Question

Consider the following degenerate elliptic equation: $$ \lambda u(x,y)-\Delta_yu(x,y)-y\nabla_x u(x,y)-b(y)\nabla_xu(x,y)=f(y), $$ where $b,f\in C_0^\infty$. Can we prove a priori estimate of the form $$ \|u\|_\infty\leq C\|f\|_{L^p(R^{2d})} ??? $$