Green's function for a certain elliptic equations with rough coefficients

We know the laplacean operator has a Green function which is smooth away from the boundary. Now, consider a linear operator of the form $\partial_i(a^{ij} \partial_j u)$.We can prove that this operator has a Green function as well. Now, if we just assume that $a^{ij} \in L^\infty$, and that $a^{ij}$ is uniformly elliptic, how much smoothness can be expected for the Green function?

Addendum: Well, we already know that away from the point on which the Dirac mass is supported, the solution is regular at least up to $C^{\alpha}$ by virtue of the theorem of De Giorgi-Nash-Moser.

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Look at the latest version of Gilbarg-Trudinger. As far as I know, it has the best results available. –  Deane Yang Sep 28 '12 at 2:32
Thanks. I'll have a look. –  S.A.A Sep 28 '12 at 23:58

Combining this with the local $C^\alpha$ estimates of De Giorgi, Nash and Moser you can get an estimate on how the $C^\alpha$ norm deteriorates when we approach the singularity.