There are good books (like Evans) for strongly elliptic second order linear PDE. I want to learn about weakly elliptic PDE (of any order). Are there any good books for the same? I am very curious as to how one could hope to find weak solutions for such PDE. I mean, the only method I know of is the Lax-milgram theorem + Fredholm alternative for compact operators. But the estimates for Lax-miligram don't work for weak ellipticty, do they?

There are good books (like Evans) for strongly elliptic second order linear PDE. I want to learn about weakly elliptic PDE (of any order). Are there any good books for the same? I am very curious as to how one could hope to find weak solutions for such PDE. I mean, the only method I know of is the Lax-milgram theorem + Fredholm alternative for compact operators. But the estimates for Lax-miligram don't work for weak ellipticty, do they? (By weak ellipticity I mean the principal symbol is an isomorphism. It isn't necessarily positive definite).