I was wondering if there are any good graduate level textbooks that go into depths on explaining PDEs in terms of distributions and their applications in mathematical physics (Schrodinger equation, Klein-Gordon equation, Green function, etc)?
I have a pretty good understanding of distribution theory and I usually use Evan as my go-to PDE textbook, but I'm not completely sure how to link the two. It would be even better if the textbook explained conditions of regularity of the solution, e.g., if PDE satisfies some conditions, then there exists a unique $C^k$ solution or something like that.