I am interested in the regularity of ellitpic equations like 

$$ -\Delta u(x) +a(x) \cdot \nabla u(x) + C(x) u(x) =f(x) \quad \Omega$$ with $ \partial_\nu u =0$ on $ \partial \Omega$  where $ \Omega=(0,1) \times (0,1)$.   

 Assuming $a,C$ and $f$ are smooth,  how much regularity can one expect for $u$.  Lets assume apriori we know $u$ is bounded and say in $H^1(\Omega)$ (say its a variational solution).   How about if we weaken $ f \in L^p$ for $1<p<\infty$.  What are the $W^{2,p}$ (and more importantly) what Holder spaces can i expect $u$ to be in.   \\ 

 
thanks