I was wondering if there were any recent references dealing with the theory of systems of elliptic PDEs: in particular, someone was telling me about something which sounded like 'Schur complementarity' and reducing a system of elliptic PDE down to one PDE, does anyone know of a recent reference which explains this theory?

I did try the book by Ladyzhenskaya but there was not that much on systems of PDE, perhaps this is quite an old reference now though.